(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "Earthquake response of fixed offshore structures."



EARTHQUAKE RESPONSE OF FIXED OFFSHORE STRUCTURES 



Owen Major Kirkley 






Library 

Naval Postgraduate School 

Monterey, California 93940 



EARTHQUAKE RESPONSE OF FIXED OFFSHORE STRUCTURES 



BY 

OWEN MAJOR KIRKLEY 

B.S., United States Naval Academy, 1958 
B.C.E., Rensselaer Polytechnic Institute, 1960 
M.S., University of Illinois, 1968 



THESIS 

Submitted in partial fulfillment of the requirements 
for the degree of Doctor of Philosophy in Civil Engineering 
in the Graduate College of the 
University of Illinois at Urbana-Champaign, 1973 



Urbana, Illinois 



7V^ 






EARTHQUAKE RESPONSE OF FIXED OFFSHORE STRUCTURES 



BY 

OWEN MAJOR KIRKLEY 

B.S., United States Naval Academy, 1958 
B.C.E., Rensselaer Polytechnic Institute, 1960 
M.S., University of Illinois, 1968 



THESIS 

Submitted in partial fulfillment of the requirements 
for the degree of Doctor of Philosophy in Civil Engineering 
in the Graduate College of the 
University of Illinois at Urbana-Champaign, 1973 



Urbana, Illinois 



Library 

Naval Postgra. ate Sch ° o1 

Monterey, SSSS ° 



111 



ACKNOWLEDGMENT 

The author wishes to thank his advisor, Professor J. P. Murtha, 
for his invaluable suggestions, encouragement, and advice throughout the 
course of this research. Acknowledgment is extended to the Department of 
the Navy for the opportunity to conduct the research, and to the Computing 
Services Office for the use of computer facilities. The author wishes to 
express his most sincere thanks and appreciation to his wife, Jean, for her 
patience, encouragement, and understanding, without which this work would 
not have been done. 



IV 



TABLE OF CONTENTS 

Chapter Page 

1 INTRODUCTION 1 

1.1 General 1 

1.2 Description of the Problem 2 

1.3 Summary of Previous Research 8 

1.4 Objective and Scope 11 

1.5 Related Topics 12 

1.6 Notation 16 

2 SINGLE DEGREE OF FREEDOM OSCILLATOR 20 

2.1 General 20 

2.2 Elastic Deformation Response Spectra ... 21 

2.3 Linearization of the Drag Force 27 

2.4 Linear Hydraulic Damping 34 

2.5 Idealized Elastic Deformation 

Response Spectrum 37 

2.6 Hydrodynamic Parameters 40 

2.7 Idealized Elastic Hydrodynamic 

Parameter Response Spectra 43 

2.8 Inelastic Response Spectra 46 

3 MULTI-DEGREE OF FREEDOM SYSTEMS 51 

3.1 General 51 

3.2 Approximate Solution of the 

Nonlinear Equations of Motion 51 

3.3 Idealized Elastic Deformation 

Response Spectra 70 

3.4 Hydrodynamic Parameters 72 

3.5 Idealized Elastic Hydrodynamic 

Parameter Response Spectra 79 

4 APPLICATIONS 80 

4.1 General 80 

4.2 Displacement Response 81 

4.3 Hydrodynamic Parameters 83 

5 CONCLUSIONS AND RECOMMENDATIONS FOR 

FURTHER STUDY 85 

5.1 Conclusions 85 

5.2 Recommendations for Further Study .... 88 



Page 

LIST OF REFERENCES 91 

VITA 215 



VI 

LIST OF TABLES 
Table Page 

1.1 Characteristics of Earthquakes Used 93 

2.1 Characteristics of Series Representation 

of Base Acceleration 95 

2.2 Comparison of Estimated |Zl „ With |Zl w 

r ' 'max ' 'max 

Computed at High Frequencies by Numerical 

Integration 96 

2.3 Distribution of Total Damping Between Structural 

and Hydraulic for Comparison Purposes 97 

2.4 Elastic Deformation Spectrum Amplification 

Factors 97 

2.5 Elastic Hydrodynamic Parameter Spectrum 

Amplification Factors 98 

2.6 Actual and Approximate Reduction Factors for 
the High Frequency Region of Inelastic Response 
Spectra. El Centro Earthquake 6 = 0.02, 

Vgmax = Q5Q 100 

3.1 Relative Values of Mass, Stiffness, and Drag 

Factor for 5 Degree of Freedom Systems 101 

3.2 Response of System 1L to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 6 = .01 102 

3.3 Response of System 1L to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 8 s = .05 103 

3.4 Response of System 1M to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 3 = .01 104 

3.5 Response of System 1M to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 3 = .05 105 



vn 



Table Page 



3.6 Response of System 2L to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 3 S = .01 106 

3.7 Response of System 2L to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. $ s = .05 107 

3.8 Response of System 2M to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 6 = .01 108 

s 

3.9 Response of System 2M to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. B $ = .05 109 

3.10 Response of System 3L to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. B = .01 110 

s 

3.11 Response of System 3L to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 3 = .05 Ill 

3.12 Response of System 4L to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. B = .01 112 

s 

3.13 Response of System 4L to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. B = .05 113 

3.14 Response of System 4M to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. B s = .01 114 

3.15 Response of System 4M to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. B = .05 115 

3.16 Response of System 4H to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. B s = .01 116 

3.17 Response of System 4H to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. B = .05 117 



Vlll 



Table Page 



3.18 Response of System 5H to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 3 = -01 118 

3.19 Response of System 5H to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 3 $ = .05 119 

3.20 Response of System 6M to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 8 = .01 120 

s 

3.21 Response of System 6M to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 3 S = .05 121 

3.22 Response of System 6H to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 3 = -01 122 

3.23 Response of System 6H to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 6 = .05 123 

3.24 Response of System 7M to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 3 = -01 124 

3.25 Response of System 7M to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. B = .05 125 

3.26 Response of System 7H to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 3 S = -01 126 

3.27 Response of System 7H to El Centro Earthquake, 
1940, N-S Component. Direct Integration 

Solution. 8 s = .05 127 

3.28 Response of System 1L to El Centro Earthquake, 
1940, N-S Component. Modal Superposition and 

Direct Integration Solutions. 8 = .01 128 

3.29 Response of System 1L to El Centro Earthquake, 
1940, N-S Component. Modal Superposition and 

Direct Integration Solutions. 6 = .05 129 



IX 



Table Page 



3.30 Response of System 4M to El Centro Earthquake, 
1940, N-S Component. Modal Superposition and 

Direct Integration Solutions. 3 = .01 130 

3.31 Response of System 4M to El Centro Earthquake, 
1940, N-S Component. Modal Superposition and 

Direct Integration Solutions. 6 = .05 131 

3.32 Response of System 7H to El Centro Earthquake, 
1940, N-S Component. Modal Superposition and 

Direct Integration Solutions. B = .01 132 

3.33 Response of System 7H to El Centro Earthquake, 
1940, N-S Component. Modal Superposition and 

Direct Integration Solutions. B = .05 133 

3.34 Hydrodynamic Parameters for System 4, Mid- 
Frequency Range. El Centro Earthquake. 

3 = .02 in Each Mode 134 

s 

4.1 Structural Properties (3 = .01 in Each Mode) 

of Towers A, B, C, and D s 135 

4.2 Estimated Linear Hydraulic Damping Ratios 

for Towers A, B, C, and D 139 

4.3 Contributions of Each Mode to the Maximum 

Base Shear. EABS Modal Combination 139 

4.4 Properties of System 4M, Mid-Frequency Range. 

3 S = .02 in Each Mode 140 

4.5 Hydrodynamic Parameters for System 4M. 

El Centro Earthquake 142 



LIST OF FIGURES 
Figure Page 



1.1 Schematic Diagram of Typical Offshore 

Structure and Lumped Parameter Model 143 

1.2 Elastic Deformation Response Spectra 

for El Centro Earthquake 144 

1.3 Ground Acceleration, Velocity, and Displacement 

of El Centro Earthquake, 1940, N-S Component ... 145 

1.4 Ground Acceleration, Velocity, and Displacement 

of Taft Earthquake, 1952, N-21-E Component .... 146 

1.5 Ground Acceleration, Velocity, and Displacement 

of Ferndale Earthquake, 1954, N-44-E Component. . . 147 

1.6 Ground Acceleration, Velocity, and Displacement 
of San Fernando Earthquake (Pacoima Dam Record), 

1971, S-16-E Component 148 

2.1 Elastic Deformation Response Spectra for 

x = 16.1 sin 2 77 t (ft/sec 2 ). 3 = 0.01 .... 149 

2.2 Elastic Deformation Response Spectra for 

x = 16.1 sin 2 77 t (ft/sec 2 ). 3 $ = 0.05 .... 150 

2.3 Elastic Deformation Response Spectra for 
Six Term Series Base Acceleration Record. 

6 S = 0.01 151 

2.4 Elastic Deformation Response Spectra for 
Six Term Series Base Acceleration Record. 

B s = 0.05 152 

2.5 Elastic Deformation Response Spectra. 

El Centro Earthquake. 6 = .00 153 

2.6 Elastic Deformation Response Spectra. 

El Centro Earthquake. 3 = .02 154 

2.7 Elastic Deformation Response Spectra. 

El Centro Earthquake. 3 = .05 155 



XI 



Figure Page 



2.8 Comparison of Elastic Deformation Response 
Spectra With Linear and Nonlinear Drag for 
Series Representation of Base Disturbance. 

3 = 0.01, K n x /K = 0.20 156 

s D g max 

2.9 Comparison of Elastic Deformation Response 
Spectra With Linear and Nonlinear Drag for 
Series Representation of Base Disturbance. 

3 = 0.05, K n x /K = 0.20 157 

M s D g max 

2.10 Comparison of Elastic Deformation Response 
Spectra With Linear and Nonlinear Drag for 
El Centro Earthquake. 3 =0.02, 

K n x n m /K = 0.50. . . s 158 

D g max 

2.11 Comparison of Linear and Nonlinear Solution. 
(Linearized by Oscillator Velocity) 

El Centro Earthquake. 3 = .00 159 

2.12 Comparison of Linear and Nonlinear Solution. 
(Linearized by Oscillator Velocity) 

El Centro Earthquake. 3 = .02 160 

2.13 Comparison of Linear and Nonlinear Solution. 
(Linearized by Oscillator Velocity) 

El Centro Earthquake. 3 = -05 161 

2.14 Linearizing Parameter for Single Degree of 
Freedom Oscillator. El Centro Earthquake. 

3 = .00 162 

s 

2.15 Linearizing Parameter for Single Degree of 
Freedom Oscillator. El Centro Earthquake. 

3 = .02. 163 

2.16 Linearizing Parameter for Single Degree of 
Freedom Oscillator. El Centro Earthquake. 

3 = .05 164 

2.17 Comparison of Nonlinear Drag Spectrum With 
Linear Drag Spectrum (Linearized by Ground 
Velocity). El Centro Earthquake. 3 =0.02, 

Vg max /K = °- 006 $ 165 

2.18 Comparison of Nonlinear Drag Spectrum With 
Linear Drag Spectrum (Linearized by Ground 
Velocity). El Centro Earthquake. 3 =0.02, 

K n x /K = 0.08 s 166 

D g max 



xn 



Figure Page 



2.19 Comparison of Nonlinear Drag Spectrum With 
Linear Drag Spectrum (Linearized by Ground 
Velocity). El Centro Earthquake. 3 = 0.02, 

K n x /K = 0.50 ? 167 

D g max 

2.20 Comparison of Linear and Nonlinear Solution 
(Linearized by Ground Velocity). El Centro 

Earthquake. 3 = 0.02 168 

2.21 Elastic Deformation Response Spectra for 

El Centro Earthquake 169 

2.22 Elastic Deformation Response Spectra for 

Taft Earthquake 171 

2.23 Elastic Deformation Response Spectra for 

Ferndale Earthquake 173 

2.24 Elastic Deformation Response Spectra for 

San Fernando Earthquake 175 

2.25 Comparison of Spectra for Two Distributions of 
Total Damping Ratio. Ferndale Earthquake. 

6 total * - 07 177 

2.26 Construction of Idealized Elastic Deformation 

Response Spectrum 178 

2.27 Elastic Hydrodynamic Parameter Response Spectra. 

El Centro Earthquake. 3. t , = 0, 1 , 2, 5, 10% ... 179 

2.28 Elastic Hydrodynamic Parameter Response Spectra. 

Taft Earthquake. $ total = 0, 1, 2, 5, 10% 181 

2.29 Elastic Hydrodynamic Parameter Response Spectra. 

Ferndale Earthquake. 3 total = 0, 1, 2, 5, 10% ... 183 

2.30 Elastic Hydrodynamic Parameter Response Spectra. 

San Fernando Earthquake. $ . , = 0, 1, 2, 5, 10% . . 185 

2.31 Construction of Idealized Hydrodynamic Parameter 

Response Spectrum for a Displacement Parameter . . . 187 

2.32 Construction of Idealized Hydrodynamic Parameter 

Response Spectrum for a Velocity Parameter 188 

2.33 Elasto-Plastic Resistance-Deformation Relationship . . 189 



xm 



Figure Page 

2.34 Inelastic (Elasto-Plastic) Response 
Spectra, El Centro Earthquake, 

3 = .02, K n x /K = 0.00 190 

s D g max 

2.35 Inelastic (Elasto-Plastic) Response 
Spectra, El Centro Earthquake, 

P s ■ - 02 ' K D X g m ax /K " °- 006 191 

2.36 Inelastic (Elasto-Plastic) Response 
Spectra, El Centro Earthquake, 

8 s ■ - 02 ' K D*g m ax /K " °- 08 ,92 

2.37 Inelastic (Elasto-Plastic) Response 
Spectra, El Centro Earthquake, 

e s ■ - 02 ' K D*g m J K " °- 50 193 

2.38 Inelastic (Elasto-Plastic) Response Spectra, 

El Centro Earthquake, 3 = .02, y = 1.5 194 

2.39 Inelastic (Elasto-Plastic) Response Spectra, 

El Centro Earthquake, 3 S = .02, y = 2.0 195 

2.40 Inelastic (Elasto-Plastic) Response Spectra, 

El Centro Earthquake, 3 = .02, y = 4.0 196 

3.1 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 1L. El Centro Earthquake, 1940, N-S 

Component 197 

3.2 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 1M. El Centro Earthquake, 1940, N-S 

Component 198 

3.3 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 2L. El Centro Earthquake, 1940, N-S 

Component 199 

3.4 Comparison of Linear Drag Solution (Linearized by 
by Ground Velocity) and Nonlinear Drag Solution. 
System 2M. El Centro Earthquake, 1940, N-S 

Component 200 



XIV 



Figure Page 



3.5 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 3L. El Centro Earthquake, 1940, N-S 

Component 201 

3.6 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 4L. El Centro Earthquake, 1940, N-S 

Component 202 

3.7 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 4M. El Centro Earthquake, 1940, N-S 

Component 203 

3.8 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 4H. El Centro Earthquake, 1940, N-S 

Component 204 

3.9 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 5H. El Centro Earthquake, 1940, N-S 

Component 205 

3.10 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 6M. El Centro Earthquake, 1940, N-S 

Component 206 

3.11 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 6H. El Centro Earthquake, 1940, N-S 

Component. 207 

3.12 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 7M. El Centro Earthquake, 1940, N-S 

Component 208 

3.13 Comparison of Linear Drag Solution (Linearized 
by Ground Velocity) and Nonlinear Drag Solution. 
System 7H. El Centro Earthquake, 1940, N-S 

Component 209 

4.1 Response of Towers A, B, C, and D to El Centro 

Earthquake, 1940, N-S Component. 3 = 0.01 .... 210 



XV 



Figure Page 



4.2 Idealized Elastic Deformation Response Spectra 
for the First Five Modes of Tower C. $ = .01 

in Each Mode ? 212 

4.3 Response of Towers A, B, C, and D Using 

Idealized Spectra 213 



EARTHQUAKE RESPONSE OF FIXED OFFSHORE STRUCTURES 

Owen Major Kirkley, Ph.D. 

Department of Civil Engineering 

University of Illinois at Urbana-Champaign, 1973 

The response of fixed offshore structures, such as those used for 
oil drilling and production purposes, to earthquake excitation is investigated. 
An approximate method of computing maximum response quantities in the structure 
is developed. The approximate method uses superposition of classical normal 
mode responses as determined by response spectrum techniques. The structure 
is modeled as a lumped parameter system, the earthquake is represented by the 
deterministic time history record of the ground acceleration, and the hydro- 
dynamic forces are considered to be those computed from Mori son's equation. 

A single degree of freedom oscillator with nonlinear drag character- 
istics is subjected to various representations of ground motion, including 
earthquake motions. The existence of a high frequency tail in the response 
spectrum is shown, and a method for linearizing the nonlinear hydrodynamic 
drag force is developed and shown to be satisfactory. A method is developed 
for conservatively estimating the magnitude of equivalent linear hydraulic 
damping in the system based on velocity characteristics of the ground motion. 
Rules are developed for the construction of idealized response spectra for 
several different response quantities. The effects of the nonlinear hydro- 
dynamic drag force on the inelastic response of the single degree of freedom 
oscillator are investigated. 

The principles and approximate methods developed during the study 
of the single degree of freedom system are applied to the multi -degree of 



freedom model of the actual structure. The linearization technique is ex- 
tended to the multi -degree of freedom system in such a manner as to insure 
the existence of classical normal modes in the equations of motion. A series 
of multi -degree of freedom systems is subjected to one of the earthquake 
records and the linearization technique is shown to be satisfactory in com- 
puting the response quantities of interest. The response of a series of 
offshore towers to an earthquake record is computed by the superposition of 
modal responses as determined by both exact spectra and idealized spectra. 
The approximate method considers the effects of the structure-fluid inter- 
action by conservatively estimating the amount of linear hydraulic damping 
developed as a result of this interaction. 



CHAPTER 1 
INTRODUCTION 
1.1 General 

The design of fixed offshore structures is frequently based on the 
static forces resulting from the loads imposed on the structure by wind, 
waves, ocean currents, and earthquakes. Design on the basis of static forces 
is satisfactory when the response of the structure is not magnified by the 
dynamic nature of the loads. However, the characteristics of the structure 
and the forces acting upon it are often such that the response of the struc- 
ture to wind, waves, currents, and earthquakes is dynamic and magnified greatly 
over the static response. In these cases, design should properly be based on 
the dynamic response of the structure. Various methods are available for cal- 
culating the dynamic response of a land-based structure to earthquake forces, 
but similar calculations for offshore structures are complicated by the pres- 
ence of nonlinear hydrodynamic forces acting on submerged portions of the 
structure. Further, these nonlinear forces are dependent not only on the 
physical characteristics of the structure, but also on the actual response of 
the structure to the forces acting on it. 

Many offshore structures are currently in use, with the most notable 
use being that of oil drilling and production platforms. While platforms in 
water depths of up to 300 feet are fairly common now, the search for new 
sources of oil and gas may result in many offshore structures situated in 
greater water depths. The location of oil resources off the coast of California, 
in the Gulf of Alaska, and other portions of the circumpacific earthquake belt 



as well as other regions of seismic activity emphasizes the need to be able 
to predict the response of offshore structures to earthquake motions. Drill- 
ing and production platforms represent a very large investment in cost, and 
large numbers of personnel are involved in the operation of such a structure. 
Failure of one of these platforms could result in many lives being lost as 
well as the loss of investment both from the cost of the platform and the loss 
of production time. 

1.2 Description of the Problem 

An offshore structure of the type mentioned in the preceding sec- 
tion is shown schematically in Fig. 1.1(a) and is a continuous system with 
an infinite number of degrees of freedom. Such structures are space frames 
composed of circular pipe sections generally welded together, with diagonal 
bracing as shown in the figure. The top portion of the structure may consist 
of more than one level and contains the heavy equipment necessary for oil 
drilling and production and often contains facilities for berthing and messing 
of the crew. The operating and production portion of the structure is gener- 
ally quite heavy. The research reported in this thesis is based on a lumped 
parameter model 1 of the structure with mass, stiffness, forces and other 
characteristics of the structure lumped into a discrete number of nodes, as 
shown in Fig. 1 .1 (b). 

The equations of motion for the system shown in Fig. 1.1(b), sub- 
jected to ground motion in quiescent water, are, in matrix form: 

rmj{x s > + [C s ]{x s - x g } + [K]{x s - x g } = {P} (1.1) 



* 

Numbers refer to List of References at end of text. 



where 

Fm-J = mass matrix of the system 

[C ] = structural damping matrix of the system 

[K] = stiffness matrix of the system 

x = absolute acceleration of node j 

x = absolute velocity of node j 
S j 

x = absolute displacement of node j 
S j 

x = ground velocity 
g 

x = ground displacement 

The symbol [* J denotes a matrix in which the off-diagonal elements are zero, 
No structural dampers are shown on the model, but the damping matrix [C ] can 
take a variety of forms as will be discussed in a later chapter. 

The hydrodynamic forces acting at each node of the system are con- 
sidered to be those computed from Morison's equation 2 for circular cylinders 
as: 



{P} = - rmj{y - [M< D J{x s |x s |} (1.2) 



where 



["m ~J = added mass matrix 3 = p["C,VJ 

p = mass density of the fluid surrounding the structure 

C, = empirical inertia coefficient at node j 
J 

V. = enclosed volume at node j 

["ICj = drag factor matrix = 2"p["CJ\J 



C n = empirical drag coefficient at node j 
J 

A. = projected area at node j 

J 

If the coordinate transformation, {Z} = {x - x }, is made, where 

^ y 

{Z} is a vector of a motion quantity of a node relative to that of the ground, 
Eqs. 1.1 and 1.2 can be combined to yield: 

[*M J{Z> + [C S ]{Z} + [K]{Z> = -rMj{x g } - rK D J{x s |x s |} (1.3) 

where 

["Mj = virtual (or total) mass matrix = ["rnj + N J 
x = ground acceleration 

Equation 1.3 differs from the equations of motion for a land-based 
structure subjected to earthquake forces in two important aspects. First, 
the presence of the added mass term causes the structure to possess natural 
frequencies and mode shapes which are different from those of a structure with 
the same stiffness and only the structural mass FmJ. Secondly, the hydro- 
dynamic force term ["K D ^]{x |x 1} is not present in the conventional land-based 
earthquake problem, and this nonlinear hydrodynamic force causes the major dif- 
ficulty in solving Eq. 1.3. 

If the nonlinear hydrodynamic force ["K D -J{x |x |}can be converted 
into an "equivalent" linear hydrodynamic force, say ["-K nL -J{x }, Eq. 1.3 can 
be written as 

^MJ{Z> + [C s ]{Z} + [K]{Z} = -FMj{x g } - rK DL J{x s } (1.4) 

Since {Z} = {x - x }, Eq. 1.4 can be rewritten as 



FMJ{Z} + [C s ]{Z} + rK DL -J{Z} + [K]{Z} 

= -^Mj{x g } - M< DL J{x g } (1.5) 

Equation 1.5 differs from the equations of motions for a land-based multi- 
degree of freedom damped structure of mass ["Mj, subjected to a base exci- 
tation, in the linear drag force D" K DL -J{x }. 

One well-known and convenient method of solving simultaneous linear 
differential equations of motion is the normal mode method. 1 In the normal 
mode method, the vector of a response quantity expressed in one coordinate 
system, such as the relative displacement between each node and the base {Z}, 
is transformed into the "normal" coordinate system by the relation 

{Z} = [<f>]{Y} (1.6) 

where 

[<J>] = a matrix of the natural mode shapes of the system with the 

ith column in the matrix representing the deflected shape 

of the ith mode of the system, 
and {Y} = a vector of modal response quantities with the ith element 

in the vector representing the modal response quantity in 

the ith mode. 

Thus, Eq. 1.6 expresses the response at each node in the model as a combina- 
tion of the responses at that node in each of the natural modes of vibration 
in the system. The natural mode shapes in the modal matrix [(J)] are orthogonal 1 , 
with respect to [*MJ and [K] and will be orthogonal with [C ] if the elements 
of [C $ ] are specified in a certain way. 21 Substitution of Eq. 1.6 into Eq. 1.5 
yields, 



FMjfoHY} + [C S ][4>]{Y> + r~K D| _J[(})]{Y} + [K][<J>]{Y} 

= -rMj{x g } - rK DL J{A g } (1.7) 

Pre-multi plying Eq. 1.7 by [<(>] yields, 

[cf)] T r-Mj[(J)]{Y} + [c})] T [C s ]U]{Y} + [4)] T rK DL J[(t)]{Y} 

+ Dl>] T [K][<t>]{Y} = -[<f>] T rMj{x g } - U] T rK D| _J{x g } (1.8) 

Recognizing the orthogonal relationships between the modal matrix [<}>] and 
other matrices in Eq. 1.8, the following matrices are defined: 

* T 

r*M ^] = [cf>] ["M -J[<})] = a diagonal modal mass matrix 

* T 

[*C J = M [C ][<(>] = a diagonal modal structural damping 

matrix. The form of [C ] which permits 
this is discussed later. 
C"K J = [<f>] [K][<J>] = a diagonal modal stiffness matrix 

[K m ] = M r*K nl J[<j>] = a modal linear hydraulic damping matrix 



V DL J LTJ L ,N DIT 



which is not necessarily diagonal 



r*w J = ["M -J" [""K -J = a matrix of circular natural frequencies 

of the system 

Using these quantites, Eq. 1.8 becomes 

C-M*.J{Y} + ^C*J{Y} + [K^_]{Y} + M(*J{Y} 

= -[«D] T ^Mj{x g } - U] T rK DL J{x g } (1.9) 



If the modal linear hydraulic damping matrix [IC. ] can be made dia- 
gonal, then the set of simultaneous differential equations of motion repre- 
sented by Eq. 1.9 will be completely uncoupled. Suppose that the nondiagonal 

matrix [K m ] can, in some satisfactory manner, be converted into a diagonal 

* 

matrix, say ["""Km -J- Then Eq. 1.9 can be written 

FM*.J{Y} + rc*^m + ITK D *J{Y} + [M<*^{Y} 



= -[>] T FMj{x g } - Df>] T rK DL J{x g } 



(1.10) 



Or, for the ith mode, 



M.. Y. + C Y. + K nl Y. + K.. Y. 
n l s.. l DL . i n i 



nn 

I 
j=l 



t-, \ji jj 



/ 



(x ) - 
9 



/ nn \ 

J-l J1 DL Jd 



(X ) 

g 



(i.n) 



where 



nn = number of nodes in the model 



Equation 1.11 can also be written as 



Y, + 23, to.. Y. + 2B. to.. Y. + uj. Y. 
i s_. n i h. n i n i 

/ nn \ / nn 
I *ji M 



j=l 



31 jj 



\ 



* 

M ii 



/ 



<V - 



■1*-1 *» \i 



11 



«.) 



(1.12) 



where 



n 



■1 2H 1fUl1 



= structural damping ratio in the ith mode 



* 

K DL.. 
$. = — * 11 = linear hydraulic damping ratio in the ith mode 

• •• 

If the modal response quantity of interest, Y, Y, or Y can be ob- 
tained from Eq. 1.12 for each mode, then the total response of the structure 
can be obtained by using the relationship given in Eq. 1.6. The modal re- 
sponse quantities vary with time, and the time variation is different for 
each mode, so an exact calculation of the total response of the structure 
can only be made if the exact time histories of the modal responses are known 
and superimposed on one another. Generally, the maximum response quantity 
at each node of the model is desired, but the modal maxima do not necessarily 
occur at the same time. An approximation to the actual maximum response at 
each node of the model can be made by determining the maximum response in each 
mode and then combining the modal responses in some fashion. The response 
spectrum is a convenient way to determine the maximum modal response. 11 " 13 

1.3 Summary of Previous Research 

Equation 1.3, or a similar form, has been solved by other investi- 
gators using various methods. Much of the existing work in this area has 
been devoted to the response of offshore structures to wave forces, but the 
nonlinear difficulties are somewhat similar for wave forces and earthquake 
forces acting on submerged or partially submerged structures. Further, the 
bulk of recent investigations has been devoted to the use of stochastic repre- 
sentations of wave and earthquake motions. 

Burke and Tighe 1 * integrate the equations of motion directly for a 
series of towers subjected to different deterministic ground acceleration 



records by using an iterative technique which computes the response quanti- 
ties of interest at step-by-step time points throughout the earthquake record. 
For a tower in 800 feet of water subjected to four accelerograms (normalized 
to the intensity of the 1940 El Centro earthquake), the effect of the water- 
structure interaction was found to reduce the maximum base shear and the maxi- 
mum overturning moment by about 33 percent from the values found when the 
water-structure interaction was not included in the solution. This method, 
while permitting the direct use of the structural properties of the system, 
including the nonlinear drag force, requires the use of a digital computer 
and the availability of actual or simulated earthquake records. For purposes 
of preliminary design of a structure for a "design" earthquake of the designer's 
choice, however, the step-by-step technique is costly, time consuming, and 
requires that a time history of the "design" earthquake be available. Pre- 
liminary design would best be served by a rapid, approximate method of solu- 
tion which permits the use of selected parameters for the design earthquake 
and accounts for the effects of the nonlinear drag forces, yet yields satis- 
factory results. 

Penzien, in association with other investigators, 6 " 8 linearizes 
the drag forces in Eq. 1.3 by replacing the nonlinear force vector with a 
linear force vector which performs the same amount of work during the history 
of the response. This linearization results in an "equivalent" linear hydraulic 
damping matrix acting on the system in much the same manner as the structural 
damping matrix acts. The linear equations of motion are then transformed into 
a normal coordinate system and solved by the normal mode method of superposition. 1 
Unfortunately, the linear hydraulic damping matrix does not uncouple when the 



10 



equations are transformed into the normal coordinate system. As a result, 
an uncoupling (or diagonal izing) technique, similar to the original linear- 
izing technique, must be employed in order to separate the equations into the 
desired modal equations. The linearizing and diagonal izing are accomplished 
by an iterative process which uses actual response quantities of the system 
as they are developed, and the procedure is time consuming and requires great 
care in its formulation and use. For towers subjected to a stochastic repre- 
sentation of the ground motion, equivalent linear hydraulic damping ratios on 
the order of 9 percent of critical are reported for the first two modes of 
towers in deep water, with "s/ery much smaller" hydraulic damping ratios for 
the tower in shallow water. 6 

Foster 9 solves the problem of an offshore tower subjected to 
stochastic representation of wave forces by linearizing the drag force, then, 
recognizing that nonproportional hydraulic damping may result, solving the 
linear equations of motion using complex eigenvalues and eigenvectors. This 
procedure recognizes that, unless the linearization of the drag force is done 
in a certain way, classical normal modes may not necessarily exist in the equa- 
tions, thus the normal mode method of superposition is not a rigorously cor- 
rect approach. 

Nath and Harleman 10 conclude that, for large diameter cylinders in 
deep water waves, the nonlinear drag force can be neglected, and, since shallow 
water structures are relatively stiff, and therefore the dynamic response to 
waves is not greatly magnified over the static response, design of shallow water 
structures can proceed on a static basis. These conclusions, however, were 
arrived at by considering the response of structures to waves, which generally 
have much longer period components of motion than do earthquakes. 



11 



1.4 Objective and Scope 

The objective of this thesis is to investigate the effects of the 
nonlinear hydrodynamic drag force on the earthquake response of single degree 
of freedom and multi -degree of freedom systems and to develop a satisfactory 
method of linearizing this force in order that conventional methods of solving 
linear differential equations may be employed in the solution of the equations 
of motion. 

A further objective is to develop an approximate method for the 
solution of Eq. 1.3 by the superposition of normal mode responses, using 
response spectra to estimate the modal response quantities necessary. A rapid, 
yet fairly accurate method of solution is desirable in the preliminary stages 
of the design of an offshore structure in order that the designer may have 
an estimate of the response of a tentative design to one or more design earth- 
quakes of his specification. It should be kept in mind that the approximate 
solution developed in this thesis is no substitute for a more detailed analysis 
of the structure once the design is in its final stages. 

In Chapter 2, the effects of the nonlinear hydrodynamic drag force 
on the response of a single degree of freedom oscillator are explored. A 
reasonable method of linearizing the drag force and a method for conservatively 
predicting the resultant linear drag effects are developed and shown. A method 
is developed for estimating certain response quantities of the oscillator in 
order to determine more accurately the range of hydraulic drag and inertia 
coefficients which should be used in the force equation. The response of the 
oscillator in the inelastic region, assuming elasto-plastic force-displacement 



12 



characteristics of the spring, is shown. Finally, the construction of ideal- 
ized response spectra, which include the effects of hydraulic drag, is shown. 

The concepts developed in Chapter 2 for the single degree of freedom 
system are extended to the multi -degree of freedom system in Chapter 3. The 
nonlinear drag force is linearized in such a manner as to insure the existence 
of classical normal modes in the equations of motion in order that normal mode 
superposition may be used as an approximate solution to the problem. The method 
of linearization is shown to be accurate for a series of five degree of free- 
dom systems which are representative of the type of structure being investi- 
gated. A means of estimating the amount of equivalent linear hydraulic damping, 
using ground motion velocity characteristics, is developed and is shown to 
yield good results. The construction of an idealized response spectrum for 
each mode of the multi -degree of freedom system is discussed and described, 
and sample problems are solved by the superposition of normal mode responses. 

The application of the approximate method to a series of actual off- 
shore towers is demonstrated, and the results of calculations of the response 
of these towers are discussed in Chapter 4. 

1 .5 Related Topics 

In this section, several topics of general interest in the field of 
earthquake engineering are briefly discussed in order that the reader may more 
fully understand the display of results by the use of response spectra, the 
numerical method of integrating the equations of motion, and the characteris- 
tics of the earthquake records used in the research. 



13 



1.5.1 Response Spectra 

The equation of motion for a damped, single degree of freedom os- 
cillator in air, subjected to a base disturbance is 

mx s + C s (x s - x g ) + K(x s - x g ) = (1.13) 

By making the transformation Z = x - x , Eq. 1.13 becomes 

mZ + C $ Z + KZ = - mx (1.14) 

Or, in an alternate form 

1 + 23 $ o)Z + w 2 Z = - x (1.15) 

The solution of Eq. 1.15 depends on the characteristics of the ground motion 
function, the amount of damping in the system as represented by the dimension- 
less parameter $ , and the natural frequency of the system, to. The frequency 
parameter enters into the solution as a dimensionless product of co and a 
characteristic time of the base motion. 13 

A plot of the maximum value of a response quantity, without regard 
to sign, as computed from Eqs. 1.13, 1.14 or 1.15, as a function of the fre- 
quency of the system is called a response spectrum for that quantity. The 
response spectrum is a convenient way to represent various maximum response 
quantities of interest as a function of the variables involved in the solution. 
The response quantity of greatest interest is usually the maximum spring dis- 
tortion, |Z| , which occurs during the response history of the oscillator, 
although other response quantities are sometimes of interest. 13 

The response spectrum is conveniently shown on tripartite logarithmic 



14 



graph paper as shown in Fig. 1.2. The grid of this representation is con- 
structed such that the abscissa represents the frequency of the oscillator, 
the ordinate represents velocity units of response, the diagonal lines 
sloping up to the right are lines of constant displacement units, and the 
lines sloping down to the right are lines of constant acceleration units. 
In this thesis, unless otherwise indicated, the response spectra shown are 
deformation response spectra in which the pseudo-velocity, w|Z| is plotted 
against the undamped frequency of the system. The displacement quantity 

shown is the maximum spring deformation, |Z| , and the acceleration quantity 

max 

?. 
is the pseudo-acceleration, u> |Z| . Response spectra for a damped single 

degree of freedom oscillator, in air, are shown in Fig. 1.2 for the El Centro 
earthquake. The shape of the spectra is typical for strong motion earthquakes 
of the type used in this thesis. More detailed information on response spectra 
can be found in the literature. 11 " 11 * 

Since the response spectra for strong motion earthquakes exhibit the 
characteristic shape shown in Fig. 1.2, the spectra can be idealized by straight 
line segments. Amplification factors, which relate the idealized spectrum to 
the ground motion quantities x , x , and x , have been developed 
for a range of damping ratios. 11 * The ability to construct an idealized repre- 
sentation of the response spectrum for a given set of conditions permits an 
estimate of the response to be made without having an actual earthquake record 
available. 

1.5.2 Numerical Integration of the Equations of Motion 

The equations of motion for a system subjected to a base disturbance 



15 



can be solved by numerical integration. In this thesis, numerical integra- 
tion of the equations of motion is performed by the Newmark "Beta Method." 5 
In the calculations, 3 is set to be equal to 1/6, thus representing the ground 
response acceleration as linear between adjacent time points. The time inter- 
val used is 1/20 of the natural period for frequencies up to 10 cps and 1/40 
of the natural period for frequencies equal to, or greater than 10 cps. These 
time increments insure good accuracy, stability and convergence in the solu-' 
tion. Convergence of the solution at any time point is assumed to have oc- 
curred if two successive iterations yield values of acceleration which are 
within 0.1 percent. In the case of multi-degree of freedom equations of 
motion, the time increment is based on the shortest natural period in the 
system, and iteration is carried out until the computed acceleration at each 
node is within 0.1 percent of the value computed on the previous cycle. In 
all cases, the integration of the equations of motion is carried out for a 
period of time equal to one-half the natural period (the longest natural 
period in the case of multi-degree of freedom systems) after the base distur- 
bance ends. 

1.5.3 Earthquake Records Considered 

Four actual earthquake records are used in this thesis. The records 
are described numerically in Table 1.1 and the time history of the ground ac- 
celeration, velocity, and displacement for each record is shown in Figs. 1.3 
through 1.6. In each earthquake record, a very small (less than .005g) arti- 
ficial acceleration point has been generated near the end of the record so 
that the velocity of the base motion is zero at the end of the record. 



16 



Although a parabolic baseline correction 16 had previously been applied to the 
acceleration records, a slight residual velocity still remained at the end of 
the record and it is this residual velocity which is removed by the artificial 
acceleration point. The four records chosen are considered to be representa- 
tive of strong motion earthquakes on firm soil. 

1.6 Notation 

As much as possible, the same symbols are used for both the single 
degree of freedom oscillator and the multi -degree of freedom system, with 
matrix and vector notation indicating the multi-degree of freedom system. 
Symbols are defined as they first appear in the text. For ease of reference 
the symbols used are summarized in this section. 

["A J projected area matrix 

Cp empirical dimensionless drag coefficient 

Cj empirical dimensionless inertia coefficient 

[C ] structural damping coefficient matrix 

L C J modal damping coefficient matrix = [<j>] [C ][<j>] 

^ s 

D diameter of a single degree of freedom oscillator 

{HDPF} vector of participation factors for hydrodynamic 

parameter response quantities 
{HDPF} = rK*^]" 1 [(f,] T [K]{I} 

{1} unit vector 



17 



[K] structure stiffness matrix 

r~K -J modal stiffness matrix = [<{>] [K][(j>] 

[^K n J drag factor matrix = 2-p["CJ\J 



{K n } modal drag factor vector for very high frequency 

system = ["M*^!' 1 ^] 1 ^ K n J{I} 



V D' 



<\j 



* 



T)" 



["KL.-J linear drag factor matrix 



[K n , ] modal linear drag factor matrix = [<j>] [""IC. -J[<}>] 

9 max dimensionless drag parameter 

["Mj total structure dynamic mass matrix = Fm-J + [~m J 



J, 



C"M J modal mass matrix = I>] FMJO] 

{P} hydrodynamic force vector 

{PF} participation factor vector for displacement response 

C^VJ enclosed volume matrix 

• •• 

{Y}, {Y}, {Y} displacement, velocity , and acceleration vectors 

{Qh (Qh {Q} in normal coordinates 

{Z}, {Z}, {Z} vectors of displacement, velocity, and acceleration 

of the structure relative to the base 

Z deformation at which yielding occurs 



18 



a relative acceleration between fluid and a single 

degree of freedom oscillator 

i subscripts indicating mode number 

j subscripts indicating node number 

["mj structural mass matrix 

F"m ^J added mass matrix = pC^C.V^J 

nm number of modes in the multi -degree of freedom system 

nn number of nodes in the lumped parameter model 

p(t) hydrodynamic force acting on the single degree of 

freedom oscillator 

v relative velocity between fluid and a single degree 

of freedom oscillator 

{x }, {x }, {x } ground displacement, velocity and acceleration vectors 
y y y 

x q max' x a max' x a max max "i mum displacement, velocity, and acceleration in 

the ground motion record 

{x }, {x }, {x } vectors of structure displacement, velocity, and 

acceleration 

y.j> y.p y. displacement, velocity, and acceleration of the ith 

q.j> q.j> q. mode single degree of freedom equation of motion 

after the modal participation factor has been taken 
out. Expressed in normal coordinates 



19 



a constant of proportionality between the linear drag 

factor ma - 



i 



factor matrix and the total mass matrix ["Kpj.-J 



6. linear hydraulic damping ratio in the ith mode 



3 structural damping ratio in the ith mode 

1 C * 

{y} vector of modal stiffness factors {y} = [(f)] [K]{I} 



ductility factor for inelastic response 
' 'max 



z y 

M mode shape matrix 

P mass density of the fluid 



ok. circular natural frequency of the ith mode 

o 2 j = rM ^"Vk ^ 



20 



CHAPTER 2 
SINGLE DEGREE OF FREEDOM OSCILLATOR 
2.1 General 

The normal mode method of solving Eq. 1.3 requires the solution 
of single degree of freedom equations of motion. For this reason, and to 
understand more fully the effects of the nonlinear hydrodynamic drag force 
on the response of a simple system, Chapter 2 is devoted to the investigation 
of the effects of the hydrodynamic drag force on the response of a single de- 
gree of freedom oscillator. 

In the investigation of the response of the oscillator with non- 
linear drag characteristics it is shown that the response of the oscillator 
in the very high frequency region can be estimated if the drag properties of 
the system are known and if the maximum velocity of the base motion is known. 
The nonlinear drag force is linearized by equating the work done by a ficti- 
tious linear force with the work done by the real, nonlinear force. This 
method of linearization is shown to be accurate until the high frequency re- 
gion of the spectrum is reached. It is shown that the linear drag force is 
equivalent to a linear hydraulic damper in which the force is dependent upon 
the velocity of the mass, and that the magnitude of the hydraulic damping 
coefficient is dependent upon the amount of structural damping in the system. 
A means of estimating the amount of linear hydraulic damping is developed 
for earthquake motions, and the estimate is shown to be conservative except 
in the low frequency range. The maximum response of the system in the mid- 
frequency range to earthquake excitation is shown to be dependent upon the 



21 



total amount of linear damping present, and not upon the ratio in which the 
damping is distributed between structural and hydraulic. 

Response quantities which may be used in order to select reasonable 
values of the inertia and drag coefficients, Cj and C D , are explored, and a 
method of estimating these response quantities is developed. The inelastic 
response of an oscillator with el as to-plastic force-displacement character- 
istics of the spring is investigated and the results are shown in the form of 
response spectra. 

The construction of idealized elastic response spectra which include 
the effects of the nonlinear hydrodynamic forces is demonstrated in this 
chapter. 

2.2 Elastic Deformation Response Spectra 

The equation of motion can be written for the single degree of 
freedom oscillator as 



MZ + C $ Z + KZ = -Mx g - K D x s |x s | (2.1) 



or 



1 + 23 wZ + Jl = -x - -£- k |x I (2.2) 

s g M s 1 s 1 v ' 



or 



Z ♦ 2B<i + U 2 Z = -« - ( K D *q ""■ )( ag_) J |J 

y g max 



(2.3) 



As pointed out in Chapter 1, the solution of the equation of motion for a 
land-based single degree of freedom oscillator (Eq. 2.1 without the nonlinear 



22 



hydrodynamic drag force ICx |x |) depends on the characteristics of the ground 
motion, the amount of damping in the system as represented by the dimensionless 
parameter 3 , and the natural frequency of the system, co. The solution of 
Eq. 2.1 depends on the magnitude of K D in addition to these parameters. A 
dimensional analysis of Eq. 2.1 yields the dimensionless drag parameter 

K D x g max 
K 

as one of the parameters on which the response of the oscillator depends. 

When using a maximum ground acceleration of 0.5 g, values of 0.01, 0.2, and 

0.6 represent a reasonable range over which to vary the dimensionless drag 

parameter. For the maximum ground acceleration in the El Centro earthquake 

record (0.312 g), values of 0.006, 0.08, and 0.50 for the parameter yield 

slightly greater variations in the magnitude of K D . Obviously, a zero value 

of the drag parameter represents a "no-drag" system and increasing values of 

the parameter represent increasing magnitudes of KL in the system for fixed 

values of K and k' m . 
g max 

Equation 2.1 is solved numerically for the steady-state maximum 
response of the oscillator when the base acceleration is 

x = 16.1 sin 2frt 

where 

2 
x is in ft/ sec 

t is in seconds 

Deformation response spectra (in which <*>|Z| is plotted against frequency) 
are plotted in Figs. 2.1 and 2.2 to show the results of the calculations. 



23 



In order to investigate the response of the oscillator to a slightly 
more complicated representation of the base disturbance, the base acceleration 
is represented as a six term cosine series. The numerical characteristics of 
the series used in the response calculations are shown in Table 2.1. The 
series has the features of zero acceleration, velocity, and displacement at 
the beginning and end of the base motion. Equation 2.1 is solved numerically 
for the maximum response of the oscillator when subjected to five cycles of 
this base disturbance, and the results are shown in the form of deformation 
response spectra in Figs. 2.3 and 2.4. 

Equation 2.1 is solved numerically for the maximum response of the 
oscillator when subjected to the El Centro earthquake record. The results 
are shown in the form of deformation response spectra in Figs. 2.5 through 
2.7. 

A study of the spectra presented in Figs. 2.1 through 2.7 reveals 

several interesting characteristics which are best discussed in terms of 

frequency ranges of the oscillator. 

In the low frequency region, the maximum spring deformation, |Z| , 

max 

approaches that for the case of K *x max /K = 0, regardless of the amount of 
hydrodynamic drag in the system for the range of drag parameter used. This 
is reasonable to expect, since the magnitude of the drag force is a function 
of the oscillator velocity, x , and very soft (low frequency) systems exhibit 
little velocity response of the mass (x ). 

In the mid-frequency region, where spectra for the conventional 
"no-drag" oscillator show an amplification of the pseudo-velocity over the 
maximum ground velocity, the spectra for systems with drag also show an ampli- 
fication of the pseudo-velocity over the maximum ground velocity. However, 



24 



the presence of the nonlinear hydrodynamic drag force causes a reduction in 
the response of the oscillator from the response of the "no-drag" oscillator. 
The amount of reduction is greater for greater values of the drag parameter 
up to some frequency. This reduction would suggest that, in the mid-frequency 
range of the spectrum, the nonlinear hydrodynamic force can be replaced by 
an equivalent linear hydrodynamic force which will effect the response in 
much the same manner as the presence of structural damping effects the re- 
sponse. The amount of reduction in response caused by the drag force is also 
seen from the spectra to be dependent upon the amount of structural damping 
in the system. This is easily noted by comparing Figs. 2.5 and 2.6. In Fig. 
2.5, the system has no structural damping, and a slight amount of drag (repre- 
sented by ICx /K = 0.006) is seen to reduce significantly the maximum 
J D g max ' a J 

response of the oscillator in the frequency range of about 1 to 10 cps. In 
Fig 2.6 the system has 2 percent structural damping, and the drag parameter 
of 0.006 is seen to cause very little reduction in the response spectrum be- 
tween 1 and 10 cps. The effects of structural damping on the amount of re- 
duction in response caused by the hydrodynamic drag are to be expected, since 
the drag force is a function of the oscillator velocity, x , and this velocity 
is a function of the amount of structural damping in the system. 

In the high frequency region, response spectra for "no-drag" oscil- 
lators typically show the pseudo-acceleration approaching the maximum ground 
acceleration, x . Response spectra in the high frequency region for the 
oscillators with nonlinear hydrodynamic force exhibit entirely different 
characteristics, however. In all the response spectra shown, a frequency is 

reached at which the maximum response quantity |Z| for the oscillator with 

1 'max 



25 



drag exceeds that for the "no-drag" oscillator. In fact, for the systems 
with larger values of the drag parameter, the quantity |Z| is seen to ap- 

1 1 id a 

proach a relatively constant value. The magnitude of this high frequency 
"tail" in the spectrum can be estimated as follows: 

Consider an undamped system with spring stiffness so great that 



s g s g 



The forces on the oscillator are 



F . = F. .. + F. 
spring inertia drag 



F Mx + K n x |x I 
spring = s D s 1 s 1 



or, 



F spring " % * K D ( */ 
Since the drag parameter 

K n x 
D q max 

K 

is held constant, K Q must increase as the spring stiffness K increases, so 
a frequency will be reached at which the inertia force can be neglected with 
respect to the drag force. If the inertia force is neglected, then 

(F ) ~ K (x )^ 
v spring 'max ~ D v g max' 

And 

(F ) K K x x 

|7| = spring 'max _D ,• x2 , p g max u g max N (9 A x 

1 'max k ~ K ^ 9 max ; l K M x ; U * 4; 

1X1X3 * g max 



26 



A comparison of |Z| obtained at high frequencies by the numerical 
integration of Eq. 2.1 with |Z| computed from Eq. 2.4 is shown in Table 
2.2 for all systems and base disturbances considered. A study of the data 
presented in Table 2.2 shows that, particularly for the earthquake records, 
the high frequency tail of the deformation response spectrum can be satisfac- 
torily estimated by the use of Eq. 2.4. 

When an acceleration record is integrated numerically in order to 

obtain the velocity and displacement records, the integration is done from 

time point to time point in the record. This double integration yields the 

values of x , = 12.79 in. /sec and x ,„ = 8.24 inches for the El Centro 

g max g max 

record as shown in Table 1.1. However, if the acceleration record is inte- 
grated to find the ground velocity and displacement at some time point which 
is between time points in the acceleration record, linear interpolation of 
the acceleration record must be performed in order to obtain the acceleration 
quantity necessary to compute the ground velocity and displacement at the 
intermediate time point. This interpolation introduces small errors into 
the acceleration, which in turn introduces slightly larger errors into the 
ground velocity which in turn introduces even larger errors into the ground 
displacement computed at the intermediate time point. 16 It was found that, 
when using the very small time increments necessary for stability and con- 
vergence in the numerical integration of the equation of motion at high fre- 
quencies (above about 8 cps), the interpolation of the El Centro acceleration 

record introduced errors into the magnitude of x such that x was found 

g g max 

to be about 14.0 in. /sec in lieu of the value 12.79 in. /sec previously ob- 
tained, even though double precision was used in all calculations. In order 



27 

to achieve comparability of results in the comparison of |ZL_„ estimated from 

max 

Eq. 2.4 and |Z| obtained at high frequencies from the integration of the 

Hlu A 

equation of motion, x a =14.0 in. /sec is used in Eq. 2.4 to obtain the 

g max 

results shown in Table 2.2 for K n x„ m /K = 0.006 and 0.08. 

u g max 

2.3 Linearization of the Drag Force 

It was seen in Chapter 1 that the use of the normal mode method to 

solve Eq. 1.3 depends on the ability to linearize the nonlinear hydrodynamic 

force vector r"K n -J{x |x 1} in a satisfactory manner. The linearization of 
u s ' s ' 

the hydrodynamic drag force in the single degree of freedom system is inves- 
tigated in this section. It is desirable to replace the nonlinear drag 
force, ICx |x |, in Eq. 2.1 by a linear drag force, say, IC. x , which will 
yield the same maximum response in the system. Consider the work done by the 
two forces: 15 



Work done by the nonlinear 

drag force over a period of time 



Work done by a linear drag 
force over a period of time 

Equating the amounts of work done, 

•t 



t 



o 
t 



(S x s l x sl)( x s )dt 



(K DL x s )(x s )dt 



t 2 

K D x s |x s |dt 



K DL x2 dt 



K D <A sl^sl > = K DL<V 

•2,- , 
/ <x s' x ^ \ 
K DL = K D ^2 ( 2 * 5 ) 

1 <x s > ' 



28 



(The symbol < > denotes the average value of the quantity enclosed over the 
time of the response of the oscillator.) This expression is the same expres- 
sion used by other investigators 6-9 to linearize a nonlinear force. With the 
nonlinear drag force replaced by an "equivalent" linear drag force, Eq. 2.1 
becomes, 

MZ + C s Z + KZ = -Mx g - K D| _x s 

MZ + C $ Z + K D| _Z + KZ = -Mx g - K D[ _x g (2.6) 



or, 



where, 



Z + 23 o)Z + 23 u o)Z + to 2 Z = -x - 23,a)X (2.7) 

s h g h g 



K DL 
B. = «j3- = equivalent linear hydraulic damping ratio 



It now remains to investigate how the maximum response in the equi- 
valent linear system compares with the maximum response in the actual nonlinear 
system. 

Equation 2.6 is solved numerically for |Zl „ using a linear drag 

max 

factor IC. which is linearized in accordance with Eq. 2.5 for the single de- 
gree of freedom oscillator subjected to the series representation of the base 
disturbance. The quantities <x | x | > and <x > necessary for the linearization 
were obtained from the integration of the nonlinear equation of motion for the 
same set of conditions. The results are plotted on Figs. 2.8 and 2.9, and it 
is seen that, for this base disturbance, the linearization is \/ery good until 
the high frequency tail begins to appear. This might have been expected, 



29 



since a linearization of a weak nonlinearity would normally be better than a 

linearization of a strong nonlinearity, and the high frequency tail is the 

result of the nonlinear hydrodynamic drag force becoming quite strong and 

dominant in Eq. 2.1 . 

A similar set of calculations is made for the El Centro earthquake, 

The response spectra for IC and IC. are shown in Fig. 2.10 for 3 =0.02 and 

KJ< , /K = 0.50. It is seen from this figure that the linearization for 
D g max 3 

the earthquake motion, while not quite as good as the linearization for the 
series representation of the base motion, is still reasonably good up until 
the high frequency tail of the spectrum is reached. A comparison of |Z| 
computed for the nonlinear drag system with |Z| for the linear drag sys- 
tern is shown in Figs. 2.11 through 2.13 for all of the variables considered. 
It is seen from a study of these figures that the maximum response of the 
linear system is close to the maximum response of the nonlinear system until 
the high frequency region is reached. The figures further indicate that the 
linearized response is slightly on the conservative side of the actual re- 
sponse until the high frequency region is reached. The accuracy of the 
linearization in the high frequency region is expected to become poor as the 
nonlinearity is becoming more and more dominant in the system, and thus the 
linearization becomes less and less equivalent. However, Eq. 2.4 permits a 
fairly good estimate to be made of the maximum relative displacement in the 
high frequency region. 

Since the linearization of the drag force in Eq. 2.1 is seen to 
yield a slightly conservative maximum response at frequencies below the be- 
ginning of the high frequency tail in the response spectrum, a method of 



30 



estimating the linear drag factor IC, from the known nonlinear drag factor 
K n is now developed for earthquake motions. A study of Eq. 2.5 shows that 
two velocity quantities, <x |x j> and <x > are necessary in order to linearize 
the drag force and, since these quantities are actual response quantities 
of the nonlinear system, they cannot be calculated a priori . A series of 
computations is macfe in which the quantity 

•2i- i 
<x sl x s l > 

is computed for the actual, nonlinear oscillator subjected to the El Centro 
earthquake. The results are shown in Figs. 2.14 through 2.16. From these 
figures it is seen that, for the range of variables studied, if the quantity 

•2,- , 

<x sl x sl > 

<> 
is estimated as 

^•2i- , 

<x x > 

g 1 q 1 

•2 

for the particular earthquake considered, then this estimated value will be 
less than the actual 

^•2i« , 

s 1 s 1 

for all frequencies except low frequencies. Using the value of 



31 



•2,- i 

<X « l \ l> 

<x 2 > 

g 

in Eq. 2.5 to linearize the drag term results in a value of IC. which is less 
than the value of IC. which would result from using the actual oscillator 
velocity quantities. When this lower value of IC. is converted into the 
linear hydraulic damping ratio, 8 h> shown in Eq. 2.7, the value of $. is 
less than the actual value of $. which would be computed had the actual os- 
cillator velocity terms been available for use in Eq. 2.5. In other words, 
linearizing the drag term by using 

•2i" i 
<x x > 

g'g 1 

-2 
<x > 

g 

in Eq. 2.5 leads to a conservative value of K D . which, in turn, leads to a 
conservative value of the maximum response in all except the low frequency 
region and the high frequency tail region of the spectrum. The unconserva- 
tive nature of IC.. in the low frequency region when computed from the ground 
velocity terms is reasonable to expect, however, as the amount of hydraulic 
damping is dependent on the velocity response of the oscillator, and wery 
soft (low frequency) systems have little velocity response, so the amount of 
hydraulic damping should approach zero as the system becomes softer and softer. 
Figures 2.14 through 2.16 further show that, for a system with given drag 
characteristics, the linear drag factor K DL estimated by using the quantity 

•2 1 • i 

g' g' 

4 



32 



becomes less conservative as the amount of structural damping increases and 
as the amount of nonlinear drag increases. The linear drag factor estimated 
in this manner does not become unconservative (except in the low frequency 
region) for the range of variables studied. 

The amount of conservatism introduced by the use of 

•2,- . 

g' g 

in linearizing the drag factor, IC, is seen in Figs. 2.17 through 2.19. In 
these figures, the spectrum for the linear drag solution is seen to be con- 
servative up until the high frequency tail begins. The linearized spectra 
were found to be slightly unconservative, as expected, in the low frequency 
region, but the scale of the figures is such that this unconservatism cannot 
easily be seen. The use of Eq. 2.4, repeated here for convenience, 

l Z Lax ■ (T^ m ax> 2 ■ <^H^>fe (2.4) 
3 g max 

is also seen to provide a yery good estimate of the nonlinear drag spectrum 

in the high frequency region. At the point in the spectrum at which the high 

frequency tail just begins to appear, the intersection of the linear drag 

spectrum with the estimate of the high frequency tail provided by Eq. 2.4 

is seen to be slightly unconservative. The amount of unconservatism in this 

transition "saddle" to the high frequency tail is reduced as the amount of 

nonlinear drag in the system increases. It is seen from the figures that, 

while linearizing the drag force by the relation, 

•2,« , 
<x x > 

K DL = K D ( -2 9 } < 2 - 8 > 

<x g > 



33 



yields conservative results in the mid-frequency region of the spectrum, the 

degree of conservatism is not so great as to be considered too conservative. 

The presence of the nonlinear hydrodynamic drag force has been seen 

to cause a reduction in |Z| from that computed for the "no-drag" oscillator 

1 'max 

at a given frequency, up until the high frequency tail region is reached. A 
measure of how much of this reduction is accounted for in the computation of 
| Z | for the system with linear drag (linearized by the ground velocity) 
is seen in Fig. 2.20. The ordinate in the figure is the ratio of the reduc- 
tion (from the "no-drag" case) in |Z| when the actual nonlinear drag force 

31 'max 3 

is used to the reduction (again, from the "no-drag" case) in |Z| when the 

3 a/i i max 

drag force has been linearized by the ground velocity terms. In Fig. 2.20, 

values of the ordinate greater than 1 represent unconservative results. The 

unconservative nature of the linearization in the low frequency region and 

the high frequency tail region is noted. While the linearization of low-drag 

systems is seen to account for less than 50 percent of the actual reduction 

ln UL av ln man y cases, the actual reduction for low-drag systems is quite 
max 

small itself, as seen in Fig. 2.17. It is further seen from the figure that 
more of the reduction in |Z| is accounted for in the high-drag systems than 
in the low-drag systems. 

Figures 2.17 through 2.20 show a measure of the amount of conserva- 
tism introduced in |Zl v by using the ground velocity characteristics to 
linearize the drag force when the structural damping ratio, 3 > is 0.02. 
For systems with less structural damping, the amount of conservatism will 
be slightly greater, and for systems with more structural damping the amount 
of conservatism will be slightly less. 



34 



2.4 Linear Hydraulic Damping 

The preceding section of this chapter has demonstrated that the 
drag factor K n can be linearized in a manner which yields slightly conserva- 
tive values of |Z| over a wide range of frequencies in the response 
max 

spectrum. The linearized drag factor, IC,, can be converted into a linear 
hydraulic damping ratio, $ h » as shown by Eq. 2.7, which is repeated here for 
convenience. 

Z + 23 wZ + 23 h ooZ + w 2 Z = -x - 23.wx (2.7) 

Equation 2.7 is seen to have the same form as Eq. 1.12 with the exception of 
the coefficients of the forces on the right side of the equation. Since the 
solution of Eq. 1.12 was shown in Chapter 1 to be necessary in order to use 
the normal mode method of solution for the response of the multi -degree of 
freedom model, the effects of 3 h on the solution of Eq. 2.7 will now be in- 
vestigated. 

Equation 2.7 is solved numerically for |Z| for all four earth- 
n J ■ 'max 

quakes with values of 3 ranging from to 0.10 and values of 3 h ranging from 
to 0.10. These ranges of 3 and 3, are considered to be inclusive of all 
reasonable values of these variables for the type of structure considered in 
this thesis. The results of the computations are shown as response spectra 
in Figs. 2.21 through 2.24. These response spectra are seen to have the same 
general shape as spectra for an oscillator without hydraulic damping until 
the high frequency region is reached. It should be noted that a high fre- 
quency tail also appears in the spectra for systems with equivalent linear 
hydraulic damping. The magnitude of this tail can be shown to approach 



35 



23 h . 

( — -)(x ) from above. However, since the equivalent linearization of the 
v a) /v g max 7 ^ 

nonlinear hydrodynamic drag force has already been shown to break down as 

the drag force becomes more dominant in the solution at high frequencies, an 

estimate of |Z| in the high frequency tail region of the spectrum for a 
max 

given system can best be made by the use of Eq. 2.4. 

Newmark et al. 11,ls,l% construct an idealized representation of 
the single degree of freedom response spectrum for an oscillator without drag 
forces by using amplication factors for displacement, velocity, and acceler- 
ation. These amplication factors are multiplied by the corresponding maximum 
ground motion quantity in order to obtain an idealized spectrum for an earth- 
quake motion of known (or assumed) values of x , x , and x . If 
^ 9 max g max g max 

amplification factors can be developed for the response spectrum of the system 
with equivalent linear hydraulic damping when 3 and 3 h are known, and the 
high frequency tail of the spectrum for the actual nonlinear system is esti- 
mated from Eq. 2.4, then an idealized response spectrum can be constructed for 
a given set of conditions for the oscillator with nonlinear hydrodynamic drag 
forces. 

During the course of establishing the amplification factors necessary 
for the construction of idealized response spectra for systems with linear 
hydraulic damping ratios (Eq. 2.7), it was found that, within the range of 
variables studied, the amount of total linear damping, 3 + 3., is the impor- 
tant factor controlling the response quantity |Z| throughout the spectrum 

max 

except for the high frequency region. Comparisons of |Z| computed from 
Eq. 2.7 at 31 frequencies from 0.04 cps to 15 cps were made for all four 



36 



earthquake records for total damping ratios equal to .02, .05, .07, .10, .12, 

and .15 with the damping being distributed between structural and hydraulic 

as shown in Table 2.3. The comparison showed that, up to the beginning of 

the high frequency tail in the spectrum, for a given value of the total damping 

ratio, |Z| computed for the first distribution of 3 and 3 U was within 5 
1 'max s h 

percent of |Z| computed for the second distribution of 3 and 3 U - Further, 
r ' 'max s n 

the great majority of the comparisons revealed a difference of less than 2 
percent between |Z| computed for the two different distributions of damping 
at a given value of the total damping ratio. The ratio 

i z U for 8 s = A - B h ■ B 



Zl for 3 = B, 3, = A 
'max s h 



was found to be sometimes greater than 1 and sometimes less than 1, indicating 
that at least a small part of the difference may be the result of the conver- 
gence criterion (0.1 percent) used in the numerical integration procedure. 

A comparison of |Z| , when 3 =0.00 and 3 U = 0.15 with |Z| when 
K ' 'max s h ' 'max 

3 = 0.15 and 3 h = 0.00 was made for each of the four earthquakes considered. 
It was found that, for frequencies up to the beginning of the high frequency 
tail of the spectrum, the value of |Z| computed for the first distribution 
of total damping was not always within 5 percent of the value of |Z| com- 
puted for the second distribution of total damping. Most of the comparisons 
differed by less than 10 percent, but a few showed differences on the order 
of 15 percent. 

The conclusion to be drawn is that, for frequencies up to the be- 
ginning of the high frequency tail region, |Z| computed from Eq. 2.7 is 

max 



37 



dependent upon the total linear damping in the system, and not the distribution 
of damping between structural damping and equivalent linear hydraulic damping 
for values of 3 h up to and including 0.10. Thus, the use of the amplification 
factors published in Ref. 14, and included in this thesis as Table 2.4, is a 
valid and proper method of constructing a portion of an idealized response 
spectrum for the single degree of freedom oscillator with drag characteristics. 

The scale of the response spectra shown in Figs. 2.21 through 2.24 
is so small that the conclusion is difficult to see from the figures. For 
illustrative purposes, a comparison of response spectra for 0. = .07 is shown 
in Fig. 2.25 for the Ferndale earthquake. It is readily seen from this figure 
that, up until the high frequency tail begins to appear, the spectral values 
are a function of the total amount of linear damping in the system, and the 
relative distribution of the total damping between structural and hydraulic 
has little effect. 

2.5 Idealized Elastic Deformation Response Spectrum 

It was mentioned in Section 1.5.1 that the characteristic shape of 
response spectra for earthquake motions has led to the development of amplifi- 
cation factors from which an idealized response spectrum can be constructed 
for a given set of conditions. The idealized spectrum permits an estimate 
to be made of the maximum response of the system. This response quantity 
may then be used as a modal response quantity for a particular mode of a 
multi -degree of freedom system, and the various modal response quantities 
may then be combined in some manner to yield an approximate solution for the 
multi -degree of freedom system as outlined in Chapter 1. 

The principles and concepts developed in Sections 2.2 through 2.4 



38 



are summarized here for the reader in such a manner as to demonstrate the 
construction of an idealized response spectrum for a single degree of freedom 
system, with nonlinear hydrodynamic drag forces, subjected to a strong-motion 
earthquake of the type used in this thesis. 

To construct an idealized deformation response spectrum for a given 



system: 



1. For the system, compute the drag factor, IC, and the undamped 
circular natural frequency of the system, u). 

2. Establish the structural damping ratio, 3 , to be used in the 
system. For the type of structure discussed in this thesis, 

a structural damping ratio of between 0.005 (when the stress 
is below one-quarter of the yield stress) and 0.05 (when the 
stress is at, or just below, the yield stress) is reasonable 
to assume. 11 * 

3. Select the values of x „ , x , x , for which the 

g max g max g max 

spectrum is to be constructed. 

4. Compute the quantity 

<x Jx l> 
K ( 9 9 ) 

D ( <x 2 > ^ 

*h " 9 

n 2 M 03 

It should be noted from Table 1.1 that the magnitude of 

^•2.: i 

<X X > 

is approximately one-half the magnitude of x for the four 

g max 

earthquakes shown. 



39 



5. Enter Table 2.4 with the value of 6 expressed as a percent, 

obtain the displacement amplification factor, multiply the 

displacement amplification factor times x „ , and plot the 
r r g max r 

result on tripartite logarithmic graph paper as a displacement 
line. This is shown as line 1 on Fig. 2.26. The method of 
linearizing the drag force by using ground velocity character- 
istics has been shown to be unconservative in the low frequency 
region. The use of 3 alone means that any hydraulic damping 
effects in the low frequency region are neglected. This is 
reasonable, however, because the small amount of velocity re- 
sponse in the low frequency region results in minor amounts of 
hydraulic damping. Further, as the frequency of the system 
becomes lower and lower, the amount of damping of any type has 
little effect on the maximum deformation. 

6. Enter Table 2.4 with the amount of total damping (3 + 3. as 
computed above) and obtain velocity and acceleration amplifi- 
cation factors. Multiply the velocity amplification factor 
times x and plot the result as a horizontal line. Multiply 

the acceleration amplification factor times x and plot the 

g max r 

result as an acceleration line. These two lines are shown as 
lines 2 and 3 on Fig. 2.26. 

7. Plot the quantity (~j<-)(x max ) as a displacement line. This 
line is shown as line 4 on Fig. 2.26. 

8. The envelope formed by the intersection of the four lines plotted 
is the idealized response spectrum for the system and conditions 
given. 



40 



With the idealized response spectrum constructed as described in 
(1) through (8) above, an estimate of the maximum response of the system is 

obtained by entering the figure with the natural frequency of the system and 

2 
reading |Z| , pseudo-velocity (u)|Z| ), or pseudo-acceleration (w l z l max )« 

If the characteristics of the system are changed, a new response spectrum 

should be constructed. 

Linear interpolation can be used to obtain amplification factors 

for values of damping not shown exactly in the table. 

2.6 Hydrodynamic Parameters 

The hydrodynamic force exerted by the fluid on the mass of the oscil- 
lator as it moves through the fluid is represented by Mori son's formula, Eq. 1.2 
as described in Section 1.2. This force expression contains two dimensionless, 
empirical coefficients, Cx and C n , which are dependent upon the response of 
the oscillator for their magnitude. Many investigators have undertaken 
studies to determine the value of these coefficients under various conditions. 
The results of some of these investigations are published and discussed in 
Refs. 17 and 18. Morison's investigations 2 show a variation of the drag co- 
efficient C n with Reynolds Number, which is related to the relative velocity 
between the mass and the fluid. Keulegan and Carpenter 19 have shown a variation 
in both coefficients with a dimensionless period parameter which can be in- 
terpreted as the ratio of the relative displacement between the mass and the 
fluid to the pile diameter for forces against circular piles. Laird 20 has 
shown that the two coefficients may vary greatly for flexible oscillating 
cylinders. Evaluation of the two coefficients for oscillatory motion is further 



41 



complicated by turbulence associated with eddy formations on either side of 
the mass as it moves back and forth through the fluid. 18 This thesis con- 



i 



siders that the drag factor, K n , and the added mass of the oscillator, m , 
remain constant throughout the entire time history of the oscillator motion. 
The values of IC and m used in the calculations in this thesis do not pre- 
suppose any specific values for C T and C~, except as values were assigned 
to these coefficients by Burke 4 in the formulation of properties of a series 
of offshore towers which are used as sample structures in a later chapter. 
However, the designer of an actual offshore structure, whose physical pro- 
perties and dimensions will eventually be known, must have a means of esti- 
mating the coefficients C, and C n with reasonable accuracy in order to analyze 
the response of his structure. Further, investigators who are engaged in 
experimental research on the response of submerged or partially submerged 
bodies to earthquake excitation should have a method of estimating the coef- 
ficients in order that the experimental work may be conducted over a reason- 
able range of variables. Since C, and C n are most commonly considered to be 
dependent upon the relative motion between the mass and the fluid, x and x 
in the case of the mass moving through the fluid at rest, a method is developed 

in this section for estimating the response quantities |x , <|x |>,|x , 

r ^ ' s'max i s 1 ' s'max 

<|x |> (hereinafter called hydrodynamic parameters) for strong motion earth- 
quakes of the type considered in this thesis. 
Consider the equations 

MZ + CZ + K n .Z + KZ = -Mx - K m x (2.6) 

s UL g DL g 

and 



42 



Z + 23 oi + 2B.coZ + to Z = -x„ - 23.wx o (2.7) 
s h g n g 

is which the nonlinear drag term K-. has been linearized in the manner dis- 
cussed previously. In the response computation, the quantities x g and x g 
may be computed at each time point from the relations 



x c = Z + x n 
s 9 



and 



x c = Z + x n 
s g 



Equation 2.7 is solved numerically for values f 3 and 3. which are reasonable 

to expect for the type of system considered, and again it is found that the 

hydrodynamic parameters |x ! ma . <|x l>, |x l av , and <|x l> are affected by 

s max s s max s 

the total amount of damping in the system and not by the distribution of damp- 
ing between structural and hydraulic. Comparisons were made of the hydro- 
dynamic parameters when the total amount of damping was equal to 2, 5, 7, 
10, 12 and 15 percent of critical with the damping being distributed between 
3 and 3. as shown in Table 2.3. The difference in a hydrodynamic parameter 
at a given value of total damping ratio is within two to five percent for the 
different distributions of damping between 3 and 3 h > thus indicating that, 
if the amount of total damping can be estimated, the parameter can be esti- 
mated. The comparison holds true for all four hydrodynamic parameters. 

Spectra for the hydrodynamic parameters Ixl , <|x |>, |x I , 
r j j r i s i max I s i I s imax 

and <|x |> are shown in Figs. 2.27 through 2.30 for total damping ratios up 
to ten percent. The general shape of the spectra indicates that an idealized 
spectrum may be able to be constructed for a given set of conditions in much 



43 



the same manner as an idealized deformation response spectrum is constructed. 
Each hydrodynamic parameter spectrum was plotted, a smooth spectrum which 
approximated the actual spectrum was established by the author, and appro- 
priate amplification factors were computed for each of the four earthquakes 
considered. These amplification factors were then averaged in a mean square 
sense to yield the amplification factors listed in Table 2.5. The use of 
these amplification factors to construct idealized spectra for the hydro- 
dynamic parameters |x , <|x |>, |x I , and <|x |> is explained in the 
J r ' s'max ' s 1 ' s'max ' s 1 

next section of this chapter. 

2.7 Idealized Elastic Hydrodynamic Parameter Response Spectra 

The construction of idealized response spectra for the hydro- 
dynamic parameters discussed in Section 2.6 is very similar to the construc- 
tion of an idealized elastic deformation response spectrum. 

2.7.1 Displacement Parameter 

To construct an approximate response spectrum for |x | (or <|x |>) 
for a given system: 

1. Determine the quantities K n , w, 3 , and 3 h in the same manner 
as described in Section 2.5. 

2. Enter the appropriate section of Table 2.5 with the value of 
3 expressed as a percent and obtain the displacement ampli- 
fication factor. Multiply this amplification factor times x 

g max 

(or <|x |>) and plot the result as a displacement line on tri- 
partite logarithmic paper. This line is shown as line 1 on 
Fig. 2.31. 



44 



3. Enter the appropriate section of Table 2.5 with the amount of 
total damping (3 + 3 h ) and obtain the velocity amplification 
factor. Multiply this amplification factor times x (or 
<|x |>) and plot the result as a velocity line as shown by 
line 2 on Fig. 2.31 . 

4. Plot the value x (or <|x |>) as a displacement line. This 

g max g 

is shown as line 3 on Fig. 2.31. 

5. The envelope formed by the intersection of these three lines 

is an idealized spectrum for |x I (or <|x |>). 
r ' s'max ' s 1 

2.7.2 Velocity Parameter 

To construct an idealized response spectrum for |x I „ (or <|x |>) 

1 s'max ' s 1 

for a given system: 

1. Obtain and use displacement and velocity amplification factors 
from the appropriate section of Table 2.5 exactly as described 
above for the construction of an idealized spectrum for a dis- 
placement hydrodynamic parameter. The resulting lines are shown 
as lines 1 and 2 on Fig. 2.32. 

2. Enter the appropriate section of Table 2.5 with the amount of 
total damping (3 + 3 h ) and obtain the acceleration amplifica- 
tion factor. Multiply this amplification factor times x 

g max 

(or < | x | > ) and plot the result as an acceleration line. This 
is shown as line 3 on Fig. 2.32. 

3. Plot the value of x (or <|x |>) as a velocity line as shown 
by line 4 on Fig. 2.32. 



45 



4. The envelope formed by the intersection of the four lines is 

an idealized response spectrum for |x I , v (or <|x |>). 
r r ' s'max ' s' 

Linear interpolation can be used to obtain amplification factors 
for values of damping not shown exactly in the table. 

Unfortunately, no reasonably consistent ratios were found to exist 

between <|x |>, <|x |>, <|x |> and other ground motion quantities such as 

x , x , x for the four earthquakes considered. Thus, the de- 
g max g max g max ^ 

signer of an offshore structure who wishes to estimate the hydrodynamic param- 
eters <|x |> and <|x |> will have to obtain the values of <|x |>, <|x |>, and 

I S l I S l I gl I gl 

<|x |> from processing an actual earthquake record or estimating them using 

the values shown in Table 1.1 as a guide. The range of the ratios between 

<|x |>, <|x |>, <|x |> and x , x , x are repeated here for the 
1 g 1 g g g max g max g max v 

convenience of the reader. 

Ratio Lowest Value Highest Value 



0.194 0.385 



0.124 0.167 



0.084 0.185 



It should be noted that the idealized spectra for hydrodynamic param- 
eters become less descriptive of the oscillator response at very low frequencies, 
about 0.08 cps and less for the four earthquakes used in the computations. This 

is to be expected, since the quantities |x » <|x |>, |x I , and <|x |> 

1 s'max ' s 1 ' s'max ' s 1 

become quite small for very soft (low frequency) systems. 



<l 


X |> 

g 


x g 


max 




• 


<| 


V* 


X 

g 


max 


<| 


V* 


x g 


max 



46 



2.8 Inelastic Response Spectra 

In this section, the effects of the nonlinear hydrodynamic drag 
force on the response of the oscillator in the inelastic range are investi- 
gated. Figure 2.33 shows the resistance-deformation relationship of the 
spring in a system with elasto-plastic spring characteristics. The character- 
istics of the elasto-plastic system are an initial elastic region, a constant 
plastic resistance limit, and an elastic unloading region. The unloading 
portion is considered to have the same slope as the initial elastic curve, and 
the unloading is elastic until yielding is reached in the opposite direction. 12 
The yield point deformation is denoted by Z , and the absolute maximum dis- 
placement of the mass relative to the base is denoted by |Z| , . The yield 

1 'max 

resistance is denoted by R . The ductility factor, y, is defined as 

y = z max (2.9) 

y 

and expresses the maximum deformation of the inelastic system in terms of its 
yield point deformation. With y defined in this manner, the maximum deforma- 
tion of the system is yZ , the maximum elastic deformation is Z , and the 
maximum inelastic deformation is (y - 1)Z . A variety of calculations of 
the response of inelastic systems has been made and reported in the litera- 
ture. 11_ltt The results of the calculations are conveniently displayed in 
the form of response spectra in much the same manner as response spectra 
for elastic systems are displayed. For elasto-plastic systems, response 
spectra can be plotted for constant values of the ductility factor, y, and 
when the plot is made in terms of the elastic component of the displacement, 



47 



the accelerations are properly presented. 12 In this type of spectrum represen- 
tation, the pseudo-velocity quantity plotted is wZ . Elasto-plastic response 
spectra for systems with 3 C = 0.02, K n x __ Y /K = 0.00 (no drag), subjected 
to the El Centro earthquake are shown in Fig. 2.34 for values of u = 1 (elastic 
case) to u = 4. In these spectra, the total deformation of the system can be 
determined by reading the displacement quantity, which is Z , and then using 
the relationship 

' 'max y y 

In the low frequency range of the spectra shown in Fig. 2.34, the 
total deformation is approximately the same for the elasto-plastic systems 
as for the elastic systems. In the high frequency region, the pseudo-acceler- 
ation is approximately the same for the elasto-plastic systems as for the 
elastic system. In the mid-frequency region, some generalizations have been 
made regarding the amount of reduction in yield level for different values 
of y, but more detailed generalizations are still under study. 12 

Elasto-plastic deformation response spectra for systems with non- 
linear hydrodynamic drag forces subjected to the El Centro earthquake are 
shown in Figs. 2.35 through 2.37. Again, in the low frequency region, the 
total deformation is approximately the same for the elasto-plastic systems 
as for the elastic system. In the mid-frequency region, the spectra have 
the same general shape as do the elasto-plastic spectra for systems without 
the drag forces, but no quantification of the results has been made. Further 
study in the direction of establishing rules for the construction of idealized 
elasto-plastic response spectra in this frequency region is clearly indicated. 



48 



In the high frequency region, the elasto-plastic spectra for the systems with 
the lowest value of the drag parameter (0.006) approach approximately the same 
values in the high frequency tail as the elastic spectrum does. However, for 
the systems with the greatest value of the drag parameter (0.50), the high 
frequency tails of the elasto-plastic spectra approach values which are re- 
duced by as much as 50 percent from the elastic case. In other words, there 
is a reduction in the magnitude of the elasto-plastic high frequency tail from 
that obtained in the elastic case, and the amount of the reduction is a func- 
tion of the amount of nonlinear hydrodynamic drag in the system. In the sys- 
tems with a small amount of drag, the reduction is yery slight, and may not 
merit much consideration, but the reduction for high drag systems can be sig- 
nificant. A study of the numerical results obtained in this investigation 

revealed that, for the spectra with 3 = 0.02, K n x /K = 0.50, values of 

K s D g max 

u up to 4 and the El Centro earthquake, the factor ~ — ^- applied to the 
elastic case high frequency tail yields a satisfactory estimate of the elasto- 
plastic high frequency tail (see Table 2.6). The reader is cautioned that 
this expression for the reduction factor is applicable only to the specific 
systems and earthquake used, and is not to be extended to other conditions. 

In order to compare the effects of the nonlinear hydrodynamic drag 
force on the elasto-plastic response spectra, spectra are plotted for given 
values of structural damping ratio, 3 , and ductility factor, u, for systems 
with varying amounts of drag subjected to the El Centro earthquake. These 
comparisons are shown in Figs. 2.38 through 2.40. These figures show that, 
for a small ductility factor (u = 1.5), increasing amounts of nonlinear hydro- 
dynamic drag reduce the value of the yield deformation, Z , for a range of 



49 



frequencies between low frequencies and the beginning of the high frequency 
tail. This means that the maximum response of the system with high drag forces 
is less than the maximum response of the system with lower drag forces, or, 
the drag forces tend to produce a damping effect on the maximum deformation 
of the spring in the mid-frequency region of the spectrum. For example, in 
Fig. 2.38, at a frequency of 1 cps, and the highest value of the dimensionless 
drag parameter used (0.50), Z is only about 50 percent of the value of Z 
for the system with no drag. However, as the ductility factor u increases, 
the effects of the nonlinear hydrodynamic drag force become less and less 
noticeable in the mid-frequency range. In Fig. 2.40, with u = 4, the value 
of Z for the highest drag system is about 90 percent of the value of Z for 
the system with no drag at a frequency of 1 cps. This is reasonable to expect, 
since the velocity of the oscillator, x , can be expected to be smaller during 
plastic deformation of the spring than during elastic deformation of the 
spring, and the magnitude of the drag force is a function of the oscillator 
velocity. It is also to be noted from Fig. 2.40 that it is possible for Z 
in the case of the system with drag to exceed slightly the value of Z for 
the system with no drag at the same frequency (note the response values at 
frequencies of 0.8 cps and 3.0 cps) in the mid-frequency range. This can re- 
sult since the maximum response of the elasto-plastic system depends on the 
entire history of the deformation and the energy absorbed in the spring during 
plastic deformation as well as the energy dissipated by the damping effects 
of the fluid surrounding the oscillator. 

The significant features of the elasto-plastic response spectra 
for systems with nonlinear hydrodynamic drag are: 



50 



1. The drag does not have much effect on the spectrum in the low 
frequency region; 

2. A high frequency tail does exist, and large amounts of drag 
can cause significant reductions in Z for increasing values 

y 

of the ductility factor (less significant reductions in Z with 
increasing values of u for low drag systems); 

3. The damping effects of the drag in the mid-frequency region 

of the spectrum become less pronounced as the ductility factor 
increases, even for the systems with high drag. 



51 



CHAPTER 3 
MULTI-DEGREE OF FREEDOM SYSTEMS 

3.1 General 

In this chapter, the principles developed and discussed in Chapter 
2 for the single degree of freedom oscillator are extended to the multi- 
degree of freedom system. The nonlinear drag forces are linearized in such 
a manner as to insure the existence of classical normal modes in the equa- 
tions of motion in order that normal mode superposition may be used as an 
approximate solution to the problem. The method of linearization is shown 
to be accurate for a series of five degree of freedom systems which are 
representative of the type of structure being investigated. A means of es- 
timating the amount of equivalent linear hydraulic damping, using ground 
motion velocity characteristics, is developed and is shown to yield good re- 
sults. The construction of an idealized response spectrum for each mode of 
the multi -degree of freedom system is discussed and described, and sample 
problems are solved by the superposition of normal mode responses. 

3.2 Approximate Solution of the Nonlinear Equations of Motion 

In this section, an approximate method of solving the nonlinear 
equations of motion for the multi-degree of freedom system is developed and 
shown to yield satisfactory results. Various features of the solution, such 
as the formulation of the structural damping matrix, the linearization of 
the drag forces, the superposition of modal responses, and the response of 
very high frequency modes, are discussed. The transformation of the nonlinear 



52 



equations of motion into uncoupled linear modal equations, which was first 
shown in Chapter 1, is repeated in this section for the convenience of the 
reader. 

3.2.1 Equations of Motion 

The equations of motion for the lumped parameter model shown in 
Fig. 1.1(b) are written in matrix form as Eq. 1.3 and are repeated here to 
form the basis of the analytical discussion in this section. 

FMJ{Z} + [C s ]{Z} + [K]{Z} = -r;Mj{x g } - rK D ^ {x s |x s |} (3.1) 

No structural dampers are shown on the model, but the damping matrix [C ] 
can take a variety of forms as will be discussed in later paragraphs. For 
a given structural system and known earthquake record, response quantities 
of interest may be obtained by the numerical integration of Eq. 3.1, but 
this procedure is costly and requires the use of a digital computer. If 
Eq. 3.1 can be satisfactorily approximated by a system of simultaneous 
linear differential equations of motion which possess classical normal 
modes, then a solution can be obtained by the superposition of normal mode 
solutions. A further approximation can be made by using response spectra 
to obtain the maximum response in each mode and then combining the modal 
maxima in some fashion, s/ery much like the approximate modal techniques, 
using response spectra, which are reported in the literature 11 " 13 for land- 
based structures. 

In the normal mode method, the vector of a response quantity ex- 
pressed in one coordinate system, such as the relative displacement between 



53 



each node and the base, {Z}, is transformed into the "normal" coordinate sys- 
tem by the relation 

{Z} = [<j>]{Y} (3.2) 

If the nonlinear drag force were not present, Eq. 3.2 and the ortho- 
gonality relationship between [<J>] and ["Mj, [K], and [C ] could be used to 
transform Eq. 3.1 into nm (number of modes) uncoupled single degree of free- 
dom equations in the normal coordinate system. If the nonlinear drag force 
can be converted into an equivalent linear drag force, then the resulting 
linear differential equations of motion can be transformed into uncoupled 
single degree of freedom equations of motion in the normal coordinate system 
as follows: Consider that ["Kn-J ^ x s l x U can De transformed into an equiva- 
lent linear force, IT" K ni ^ {**} i.e., 

n< D ^]{x s |x s |} - rK D| _J (x s > (3.3) 

Substitution of Eq. 3.3 into Eq. 3.1 yields, 

FMJ{Z} +[C S ]{Z}+ [K]{Z} = -FMj{x g } - [-K DL J{x s } (3.4) 
Since {Z} = {x } - {x }, Eq. 3.4 can be rewritten as 

[^MJ{Z} + [C S ]{Z} + rK DL -J{Z} + [K]{Z} 

= -FMj{x g } - rK D1/ J{x g } (3.5) 

Substitute Eq. 3.2 into Eq. 3.5 and premultiply the result by M 



54 



MVmJEcDKY} + [cj)] T [C s ][(()]{Y} + [<f>] T rK DL J|>]{Y} + [<f>] T [K]|>]{Y} 
= -U]VMj{x g } - [<f)] T rK DL -J{x g } (3.6) 

Recall the following definitions from Chapter 1: 

* T 

C"M -J = [<J>] M[(J>] = a diagonal modal mass matrix 

* T 

[~~C -J = M [C ~\M = a diagonal modal structural damping 

matrix. The form of [C ] which permits 

this is discussed later. 

* T 

["K ~J = [<|>] [K][<|>] = a diagonal modal stiffness matrix 

% T 

[K n( ] = [<j>] C~~ Kpj. -J[<{>] = a modal linear hydraulic damping 

matrix which is not necessarily 
diagonal 
C"oo J = [*M ^] ["K ~J = a matrix of circular natural fre- 
quencies of the system 

Substitution of these definitions into Eq. 3.6 yields 

FM*J{Y} + rC*^]{Y} + [Kp L ]{Y} + rK*J{Y} 

= -Dofr-MjCXg} - [(0] T rK DL J{x g } (3.7) 

At this point, the formulation of the structural damping matrix, [C ], and 
the linearization of the drag factor, r~Kn-]> will be discussed. 

3.2.2 Structural Damping 

If the structural damping matrix [C ] is proportional to the mass 



55 



matrix, then [~C -J will be diagonal since the natural mode shapes are ortho- 
gonal with the mass matrix. This formulation of [C s ] results in modal damping 
ratios which decrease with increasing natural frequency. This is shown as 
follows: 
Let, 

[C ] = CFMJ 



then, 



Define 



then, 



where 



[4)] T [C s ][d>] = S[<J>] T ^Mj[cf>] = cr-M*^] = rc*J (3.8) 



rM*J _ Vc*^l = r~23 s o)J = ?[I] (3.9) 



3 = o*— (3.10) 

2w ii 



$ = structural damping ratio in the ith mode 
s i 

a>. . = circular natural frequency of the ith mode 

In a similar manner, it can be shown that, if the structural damping 

•k 

matrix [C ] is proportional to the stiffness matrix [K], then [~ C J is a 
diagonal matrix in which the modal damping ratios 3c increase with increasing 
frequency. 

The elements of the structural damping matrix [C ], can be selected 
to yield the same structural damping ratio in each mode. It is common prac- 
tice to assume the same structural damping ratio in all modes in the dynamic 



56 



analysis of damped multi-degree of freedom systems. 12 If the modal matrix 
[<{>] is normalized such that 

[4>] T rMJ[>] = [MJ (a unit matrix) (3.11) 

Then 

[C s ] = C-MJU]rc*J[(D] T |^Mj (3.12) 

And, since 

r^ = ^M*^r2e s o J J (3.13) 

Equation 3.12 can be written as 

[C s ] = rMj[4>]rM*^jr23 s ooJ[cJ>] T rMj (3.14) 

Thus, it is seen that [C ] can be formulated in such a manner as 
to yield modal structural damping ratios which are constant, which increase 
with increasing mode number, or which decrease with increasing mode number. 
In the computations reported in this thesis, the structural damping matrix 
[C ] is computed in such a way that 3 is the same in all modes. 

3.2.3 Linearization of the Drag Force 

Foster, 9 and Malhotra and Penzien 6 linearize the nonlinear drag 
forces, ["HL-J{x |x |} by replacing them with a velocity dependent linear 
force, r~K D . -J{x } at each node which performs the same amount of work during 
a period of time as does the nonlinear force at that node. Foster then 
recognizes that the resulting [""K^.-J matrix is not orthogonal with the mode 
shapes and proceeds to solve the equations of motion by a nonclassical mode 



57 



approach using complex eigenvalues and eigenvectors. Malhotra and Penzien 
transform ["K m -J into [K n| ] and then force [K R| ] to be diagonal by means 
of an iterative process that replaces the nondiagonal matrix with a diagonal 
matrix which dissipates the same amount of energy over a period of time. 

The hydraulic drag forces, whether linear or nonlinear, may be con- 
sidered to act as dampers, that is, they cause energy to be dissipated as 
the system oscillates through the fluid. In the approximate solution being 
developed in this section, the nonlinear dampers in the multi -degree of 
freedom system are replaced with linear dampers (except for \/ery high fre- 
quency modes which are discussed in a later section) which dissipate the 
same amount of energy over the total system, but do not necessarily preserve 
the dissipation of energy at each node. Further, the resulting "equivalent" 
linear damper at each node is made to be proportional to the lumped mass of 
that node in order that the modal equations of motion will be uncoupled. For 
an offshore structure with a portion of the structure above the water line 
as shown in Fig. 1.1(a), this procedure results in a linear hydraulic damper 
being provided at the level of the top mass where, in fact, no nonlinear 
hydraulic damper really exists. With this exception, the proportioning of 
the linear hydraulic dampers in the same ratio as the mass is distributed is 
a reasonable approach for the type of structure being discussed, since the 
nonlinear damper is proportional to the projected area of the structure lumped 
at the node, and the magnitude of the mass at a given node will also be gen- 
erally proportional to the projected area. The method of linearizing is as 
follows: 



58 



nn 



t 



Energy dissipated by = (K n x |x |)(x ) dt 

nonlinear dampers >-, 



o 



D.. s. 1 s . ' s- 
JJ J J 3 



nn 9 

= t 7 K n <)C |x |> (3.15) 

• S D. . s . ' s • ' 

J=l JJ J J 



Energy dissipated by nn 
equivalent linear = £ 



(K nl x )(x ) dt 
v DL . . s . s. 



dampers j = l J jj j j 



= t f K DL <x*> (3.16) 

J=l JJ J 

where 

nn = number of nodes in the system 
j = jth node in the system 

Equating the energy dissipated, 

nn 9 nn ? 

I K <k l l*s \ y = I K DL K K > (3J7) 

j=l °jj S j S j J=l Jj S j 

It is noted that only the total energy dissipated is preserved and the dis- 
tribution of the energy dissipation among nodes is not preserved. Now, by 
forcing the linear dampers to be proportional to the mass matrix, 

rK DL ^J = aC^Mj (3.18) 



and substituting Eq. 3.18 into Eq. 3.17 



59 



a = 



nn ~ 

J=l JJ J J 
nn .o 

y m.. <x c > 



(3.19) 



Recall that [K^] was defined as U]Vk dl ~J[>]. Substituting Eq. 3.18 into 
this definition, 

[K^_] = a[<D] T rMj[>] = afM*.J (3.20) 

Substituting Eq. 3.20 into Eq. 3.7 yields 

r-M*J{Y} + |^C*J{Y} + a^M*J{Y} + [~ K*J{Y} 

= [*] T |^MJ{-x g - ctx g } (3.21) 

Equation 3.21 represents nm single degree of freedom uncoupled equations of 
motion in the normal coordinate system. 

Before proceeding, the method of linearizing described by Eqs. 3.18 
and 3.19 will be tested for accuracy in computing the response of multi -degree 
of freedom systems to earthquake excitation. A series of five degree of free- 
dom systems, representative of offshore towers in mass, stiffness, and drag 
distribution, is developed in order to test the linearization technique. 

Seven structural systems, consisting of different combinations of 
mass and stiffness distribution, are considered. Each system is further 
subdivided into one or more distributions of the drag factor, K n , at each node. 
The characteristics of these systems are shown in Table 3.1. In the table, 
the values shown for the mass at each node are considered to be the total 
mass at that node, and include the added mass term. The different 



60 



distributions of drag factor are labeled L, M, and H in the table, and the 
column under each of these headings represents the relative magnitude of IC 
at each node for the particular distribution shown. For example, drag factor 
distribution M represents the distribution of K Q at each node as 0, 1, 1, 2, 
3 at nodes 1 through 5 respectively. The values of ZKL/Zm shown in the 
table for the distributions of drag factor are of sufficient range to span 
reasonable values of this quantity for actual offshore towers of the type 



being investigated. The quantity IIC/Em for the four towers reported by 
Burke and Tighe" range from a low of 0.0034 inches" to a high of 0.0054 
inches" . The relative magnitudes of the undamped natural frequencies of 
the system, normalized to the fundamental frequency, are as shown. In the 
computations which are discussed in the following paragraphs, one of the 
natural frequencies is set to a desired value and the fundamental frequency 
is computed from the ratio of natural frequencies. The value of k, is com- 
puted from f, and the quantity f,//k,/m, , then the remaining spring stiffnesses 
are computed from k, and the distribution of k ? through k^. The stiffness 
matrix [K] for the entire system is then assembled and is a tri -diagonal 
matrix for the systems shown. 

Each of the systems shown in Table 3.1 is subjected to the El Centro 
earthquake and response quantities are computed by the numerical integration 
of the equations of motion using the criteria for convergence and time inter- 
val described in Chapter 1. For each system, computations of maximum re- 
sponse are made for two values of 3 in each mode, 0.01 and 0.05, and three 
frequency ranges. The low frequency range, range number 1, is established 

by setting the fifth natural frequency equal to the frequency at which x 

g max 



61 



and x intersect when plotted on tripartite logarithmic paper. The 
a g max 

mid-frequency range, range number 2, is established by setting the funda- 
mental frequency equal to the frequency at which x and x inter- 
sect. The high frequency range, range number 3, is established by setting 
the fundamental frequency equal to the frequency at which x and x 
intersect when plotted on tripartite logarithmic paper. The maximum dis- 
placement of each node relative to the base, {|Z| }, is computed. The 

max 

results of the computations are shown in Tables 3.2 through 3.27. The 
column in the tables titled "No Drag" shows the results of the computations 
when ["K^-J is set to zero. The column in the tables titled "Actual Drag" 
shows the results of the computations when ["^.J is computed from the values 
shown in Table 3.1, thus nonlinear hydrodynamic drag forces, [""K n ^]{x |x |}, 
are acting on the structure. In the computations for the "Actual Drag" 
systems, the time averages {<x |x |>} and {<x >} are collected. These time 
averages are then used to linearize the drag factor and set it to be pro- 
portional to the mass matrix as prescribed by Eqs. 3.18 and 3.19. Equation 
3.4, using the linear drag factor matrix just computed, is then integrated 

numerically to obtain the response quantity {|Z| }. The results of this 
* v M J ' 'max 

integration are labeled "Case 1" in the tables of results. The column 
labeled "Case 1/Actual Drag" in Tables 3.2 through 3.27 represents the com- 
parison of the solution of Eq. 3.1 with the solution of Eq. 3.4. A study 
of these results reveals that the linearization technique described by Eqs. 
3.18 and 3.19 is extremely accurate. The difference between the linear and 
the nonlinear results is less than 6 percent (with one exception — system 1M, 
3 S = 0.01, node 3, mid-frequency range) and is less than 2 percent in the 
majority of the cases. 



62 



The maximum distortion between two adjacent nodes is also computed 

for both the linear and the nonlinear equations of motion. The results of 

the computations for the linear case in which the linearization is carried 

out according to Eqs 3.18 and 3.19 are not shown in this thesis, but the 

linear solution is as close to the nonlinear solution as for the response 

quantity {|Z| } shown in the tables. Thus, it is concluded that the meth- 
max 

od of linearizing the drag force described by Eqs. 3.18 and 3.19 yields 
satisfactory results. 

The primary difficulty in using Eqs. 3.18 and 3.19 to linearize the 

•2, • 
drag force lies in the ability to determine the quantities {<x |x |>} and 

• 2 
{<x >} a priori . If these quantities can be estimated in some fashion, and 

if the estimate can be shown to be accurate in certain frequency ranges, 
then Eq. 3.1 can be linearized into Eq. 3.4, and Eq. 3.4 can be transformed 
into uncoupled, modal, single-degree of freedom equations in the normal co- 
ordinate system which can be solved by spectrum techniques. It was demon- 
strated in Chapter 2 that, for the single degree of freedom oscillator, the 

•2. • , *2 
quantities <x x > and <x > are conservative estimates of the oscillator 

g 1 g 1 g 

velocity in all but the low frequency region of the spectrum. Since the 
major effects of hydraulic damping occur in the velocity amplification re- 
gion of the spectrum, it seems reasonable to estimate the quantities 

t |x |>} and {<x >} as {<x 
quantities, Eq. 3.19 becomes 



{<x |x |>} and {<x >} as {<x |x |>} and {<x >} respectively. Using these 



a = 



/ T V \/<x^|x g |> 

(3.22) 



j=l j> 



nn 



1 
\ j=l 



•2 

i . / \ ^x 

jj / \ g 



M.. / \ <x_ > 



63 



A series of computations, labeled "Case 2" in Tables 3.2 through 3.27, is 
made in which the nonlinear drag factor is linearized in the manner pre- 
scribed by Eqs. 3.18 and 3.22. A study of the column labeled "Case 2/Actual 
Drag" shows that the linearization described by Eqs. 3.18 and 3.22 is, in 
general, conservative in the mid and high frequency ranges and is generally 
unconservative in the low frequency range. The degree of conservatism in 
the mid-frequency range is seen to be less than 5 percent in most cases, 
although one case is conservative by 12 percent. In the high frequency 
range, the results are seen to be conservative by as much as 20 percent in 
some cases, especially in the high drag systems, but many of the results are 
conservative by less than 10 percent in the high frequency range. The degree 
of unconservatism in the low frequency range is seen to be less than 10 per- 
cent in most cases, but can range as high as 23 percent. This unconservatism 
in the low frequency range is to be expected, since very soft (low frequency) 
systems can be expected to exhibit little velocity response at each node, 
and so the use of the ground velocity characteristics overestimates the 
velocity of each node. One further observation to be made from a study of 
the numerical results is that the use of the ground velocity to linearize 
the drag force is generally more conservative as the response is reduced 
to a greater degree by the actual nonlinear drag force. In those cases in 
which the Case 2 linearization is unconservative in frequency ranges 2 and 
3, the degree of unconservatism is generally very slight (less than 1 percent). 

The maximum deformation between adjacent nodes is also computed 
and a comparison of the linear drag response (linearized by the ground velocity 
characteristics) with the nonlinear drag response is shown in Figs. 3.1 



64 



through 3.13. These figures show that the maximum spring deformation com- 
puted when the drag force is linearized by the ground velocity characteristics 
is also conservative in the mid and high frequency ranges and generally un- 
conservative in the low frequency range. It is concluded from these compu- 
tations that the use of Eqs 3.18 and 3.22 is a reasonable way to linearize 
the drag force and yields slightly conservative results except in the low 
frequency range. The conservatism introduced by the linearization is seen 
from the figures to be generally less than 10 percent in the mid and high 
frequency ranges, with some of the results in the high frequency range being 
conservative by as much as 20 percent. The results of the low frequency range 
calculations are generally unconservative by less than 20 percent, but can be 
unconservative by as much as 25 percent. 

The effect of structural damping on the response is quite apparent 
from the tables and figures. For example, the maximum relative displacement 
between the bottom node (mass number 5) and the ground for system 4M in fre- 
quency range 2 is reduced approximately 17 percent by the hydraulic drag when 
the structural damping ratio is 0.01 in each mode (see Table 3.14). Yet the 
response is reduced by less than 2 percent by the hydraulic drag when the 
structural damping ratio is 0.05 in each mode (see Table 3.15). Thus, the 
selection of structural damping ratios to use in the response computations 
is seen to be yery important. 

3.2.4 Modal Equations in Normal Coordinates 

The use of Eqs. 3.18 and 3.22 to linearize the drag force has been 
shown to yield generally conservative results in the mid and high frequency 



65 



ranges, and unconservative results in the low frequency range. Since the 
linearization prescribed by Eqs. 3.18 and 3.22 insures that the equations of 
motion for the linearized system (Eq. 3.5) will possess classical normal modes, 
the discussion of the superposition of normal modes is resumed. Recall the 
uncoupled equations of motion in the normal coordinate system. 

= W T r-M^{-x g - ax g } (3.21) 

_ * i 
Premulti plying by [/M -~J yields 

{Y} + r~23 s u)J{Y} + r26 h wJ{Y) + 2 J{Y} 

= rM*^I" 1 [(D] T C-Mj{-x g - ax g } (3.23) 

where 

aMJ = C^w-J (3.24) 

The terms on the right side of Eq. 3.23 can be written as 

r-M*^ _1 [(})] T [-Mj{-x g - ax g } = {PF}(-x g - ax g ) (3.25) 

where 

{PF> = ^M^^M^Mjd} (3.26) 

and PF. is the participation factor for the ith mode. Substituting Eq. 3.26 
into Eq. 3.23 

{¥} + r'2S s o)J{Y} + F26 h o)J{Y} + [> 2 J{Y} 

= {PF}(-x g - ax g ) (3.27) 



66 



For the ith mode, then, 

Y. +23 co..Y. + 23 u to.-Y. + o>?.Y. = PF.(-x -ax) (3.28) 

i s. n i h. n i n i i g g 

11 3 3 

Since the left side of Eq. 3.28 is linear with respect to the unknown Y, the 
maximum modal response in the ith mode can be obtained by determining the 
maximum response of the single degree of freedom equation, 

y i ♦ 2^0,,..^ + ZB^a,,*, ♦ ^.y. = -x g - ax g (3.29) 

and multiplying this response times the participation factor for the ith mode, 
PF.. The nonlinear equations of motion for the multi -degree of freedom system, 
Eq. 3.1, have now been transformed into a set of linear simultaneous differ- 
ential equations (Eq. 3.5) by the use of Eqs. 3.18 and 3.22. The linear 
simultaneous differential equations are transformed into nm uncoupled, single 
degree of freedom modal equations of the form represented by Eq. 3.28 in the 
normal coordinate system Y by the use of Eq. 3.2. The total response of the 
system is the result of a combination of the various modal responses represent- 
ed by Eq. 3.28. 

3.2.5 High Frequency Modes 

The existence of a high frequency tail in the response spectrum 
for a single degree of freedom oscillator was demonstrated and discussed in 
Chapter 2. Further, the linearization of the nonlinear hydrodynamic drag 
force was shown to break down when this high frequency tail began to appear. 
A method for determining the parameters necessary to estimate the magnitude 
of this tail for each mode in the multi -degree of freedom system is now 



67 



developed. Consider the equations of motion for an undamped multi -degree of 
freedom system 

r*Mj{Z) + [K]{Z> = -FMj{x g } - rK D J{x s |x s l> (3.30) 

If the system is so stiff that {x } s (x „}, Eq. 3.30 can be written as 

s g 

C^MJ{Z} + [K]{Z> = -^Mj{x g } - rK D J (x g |x g |} (3.31) 

Transform Eq. 3.31 into the normal coordinate system by the use of Eq. 3.2 
and premultiply by [<j>] 

[*] T rMj[<J>]{Y} + [<J>] T [K][<j>]{Y} 

= -W T rM^]{I}x g - [(f»] T rK D -J{I}(x g |x g |) (3.32) 

or, 

r-M*^j{Y} + rK*j{Y> 

= -E*] T [^Mj{I}x g - [c|»] T rK D -J{I}(x g |x g |) (3.33) 

Equation 3.33 represents nm single degree of freedom uncoupled modal equations 
in normal coordinates for the high frequency multi-degree of freedom system. 
Premultiply Eq. 3.33 by C^M*^]" 1 , then 

{Y} + [> 2 J{Y} = -{PF}x g - '{KJj}(x g |x g |) (3.34) 



where 



{K*} = C-M^'^iDflMCnJII} (3.35) 



For the ith mode then, 



68 



K D. 

Y. + coT.Y. = PF. (-x - of 1 x |x I) (3.36) 

i n i i v g PF i g 1 g" 

Again, since the left side of Eq. 3.36 is linear with respect to the unknown 
Y, the maximum modal response in the ith mode can be obtained by determining 
the maximum response of 

K D. 

y. + o) 2 .y. = -x - ■==! x |x I (3.37) 

J i n J i g PF i g 1 g 1 

and multiplying this response times the participation factor for the ith mode. 

It was shown in Chapter 2 that the quantity ly. | maw can be estimated for 

i max 



Eq. 3.37 as 



y • 
lJ -\ 'max 



PF. 

l / • \ 2 



2 * g max 



\ w ii M ii 



(x„ ma J 0.38) 



and 



Y.l = (PF.)(|y.| ) (3.39) 

l'max v -r^i'max' 



3.2.6 Superposition of Modal Responses 

The maximum response in any given normal mode of the multi -degree 
of freedom system can be computed from Eq. 3.28. However, the maximum re- 
sponse in one mode does not necessarily occur at the same time as the maximum 
response in another mode, and the time of occurrence of the maximum response 
in the time history of the modal response is not normally known. The actual 
combination of modal responses in a multi -degree of freedom system is very 
complex and few generalities can be made about the combination. 



69 



An approximation to the actual maximum response of a multi -degree 
of freedom structure can be made by determining the maximum response in each 
mode, and then combining the maximum modal responses in some fashion. An 
upper bound on the maximum response of the structure can be established by 
assuming that the maximum modal responses occur at the same time in each 
mode and are additive in nature. In other words, the summation of the ab- 
solute values of the maximum response in each mode yields an upper bound to 
the response of the structure. Another commonly used method of combining the 
maximum modal responses is to take the square root of the sum of the squares 
of the modal responses. Other methods of combining modal responses are some- 
times used. 22 The two most commonly used methods are the summation of the 
absolute values of the modal maxima (ZABS) and the square root of the sum 
of the squares of the modal maxima (SRSS). These two methods are the only 
ones used in this thesis for illustrative purposes. Tables 3.28 through 
3.33 show the results of the superposition of maximum modal responses applied 
to three of the five degree of freedom systems. The drag force is linearized 
in accordance with Eqs. 3.18 and 3.22 (ground velocity linearization), and 
the amount of linear hydraulic drag $. in each mode is computed from Eq. 3.24. 
The maximum modal response in each mode is computed from the response of the 
single degree of freedom modal equation (Eq. 3.29), and multiplied times the 
participation factor for the mode. The SABS combination is seen to be higher 
than the true response (as should be the case) and the SRSS combination is 
generally less than the true response. No generalizations as to the relative 
accuracy for different distributions of mass, stiffness, and drag factor can 
be made, however. 13 Thus, it is seen that, if the maximum responses of the 



70 



single degree of freedom modal equations, Eq. 3.28, can be computed, the maxi- 
mum response of the structure can be approximated by a combination of the 
modal maxima. 

3.3 Idealized Elastic Deformation Response Spectra 

It was seen in the preceding section that the maximum response of 
a multi -degree of freedom system can be approximated by combining maximum 
modal responses in some fashion. If the maximum modal responses can be esti- 
mated in a way that accounts for the effects of the nonlinear hydrodynamic 
drag forces in the system, a rapid approximation of the response of the sys- 
tem can be obtained. The principles developed in Chapter 2 for the single 
degree of freedom oscillator and the method of linearizing the drag forces 
developed in this chapter can be combined to construct an idealized elastic 
deformation response spectrum for each mode of the multi -degree of freedom 
system subjected to strong motion earthquake excitation. The procedure for 
the construction of the modal elastic deformation response spectra is now set 
forth. 

1. Compute the natural frequencies, ["wj, and mode shapes, [<|>], 
for the system. 

2. Establish the structural damping ratio, $ s ., for each mode. 
Values of 3c. between 0.005 and 0.05 are reasonable to assume 
for the type of structure being investigated in this thesis. 

3. Determine x , x , x , and 

g max g max g max 

•2,- , 

g 1 g 1 

•2 



71 



for the earthquake to be used. If the spectra are to be con- 
structed for a hypothetical or "design" earthquake, one-half 

of the value of x is a reasonable value to assume for the 
g max 

quantity 

g' g 

<> 

Compute M.., Kq , PF., a, 3 n ., and the high frequency tail 
estimate from the following expressions: 



FmVj = W^MJW 



(k*} = ^^Wr^m 



{PF} = rM*^]- 1 [ ( {)] T [^Mj{I} 



(3.35) 
(3.26) 



/ i 



a = 



J-l D .1.1 



nn 



I M.. 
\ j=l JJ 




(3.22) 



r23 h o)J = a[-IJ 



(3.24) 



High Frequency Tail 
Estimate for the ith = 
Mode 



TJ. 
l 



PF 



l 



2 * 
uf.M. 



| / 



^ x g max^ 



(3.38) 



5. 



With the quantities to.., $ s ., 3h.» and the high frequency tail 
estimate, construct the idealized elastic deformation response 



72 



spectrum for the ith mode exactly as described in Section 2.5 

for the single degree of freedom system. 
It is noted that the idealized response spectrum constructed as 
outlined above accounts for the fluid-structure interaction in a slightly 
conservative manner. When an idealized spectrum has been drawn for each mode 
of the system, the maximum modal responses are obtained from the spectra, 
multiplied times the appropriate modal participation factor, and combined in 
some manner to yield an approximate maximum response of the system. 

3.4 Hydrodynamic Parameters 

An approximate method for computing hydrodynamic parameters for a 
multi-degree of freedom system by the superposition of normal mode responses 
is developed in this section. As explained in Chapter 2, these hydrodynamic 
parameters are absolute displacement and velocity responses of the mass (each 
node in the multi-degree of freedom system), whose magnitudes are desirable 
to know in order that the empirical drag and inertia coefficients, Cq and Cj, 
may be estimated in a reasonable way. The hydrodynamic parameter spectrum 
amplification factors developed in Chapter 2 may be used to construct idealized 
spectra from which the response quantity of interest in each mode can be esti- 
mated. 

Consider again the linear equations of motion, 

r*Hj{Z} + [C s ]{Z> + [K]{Z} = -FMj{x g } - rK DL J{x s ) (3.4) 

Making the substitution {Z} = {x } - {x }, Eq. 3.4 can be written as 

s g 



73 



FMj{x s } + [C s ]{x s > + rK D| _J{x s > + [K]{x s > 

= [K]{x g > + [C s ]{x g > (3.40) 

If the velocity force, [C ]{x }, can be dropped from Eq. 3.40 for values 
of [C ] up to some magnitude without unreasonable loss of accuracy in the 
solution (this is discussed in subsequent paragraphs of the section), and 
the drag factor matrix ["* IC. J is made to be proportional to the mass matrix 
[""Mj, then Eq. 3.40 can be written as 

FMJ{X S ) + [C s ]{x s > + a[-Mj{x $ } + [K]{x s > = [K]{x g } (3.41) 

In order to transform Eq. 3.41 into a "normal" coordinate system, the trans- 
formation 



{x s > = [4>]{Q} (3.42) 

is made. Substituting 3.42 into Eq. 3.41 and premulti plying the result by 

of, 

= [4>] T .[K]{x„} (3.43) 



Define 



g 



(Y> = l>] T [K]{I} (3.44) 



and Eq. 3.43 can be written as 



Fm\J{Q} + rC*J{Q} + arM*^J{Q} + r~K*J{Q} = { Y }x n 
*> y 



(3.45) 



74 



Equation 3.45 represents nm uncoupled single degree of freedom modal equations 
of motion. The equation of motion for the ith mode is 

M*.Q. + C* Q. + aM*.Q. + K*.Q. = y.x (3.46) 

n v i s..j i n x i n i 'i g v 

or, 

<J1 + 2 %«A + Z \«iA + «fal ■ (^ ><<4i X g> (3-47) 

Since the left side of Eq. 3.47 is linear with respect to the unknown Q, the 
response quantities of interest in the ith mode can be obtained by computing 
the desired response quantities from 

9 9 

q + 26 coq + 23 h coq + oo q = oi x (3.48) 

and multiplying the result times the ith mode participation factor for hydro - 
dynamic parameters . The participation factor for hydrodynamic parameters 
can be seen from Eqs. 3.44 and 3.47 to be 

{HDPF} = FK^LclOVin} (3.49) 

Once the modal quantities are obtained in the Q coordinate system, Eq. 3.42 
can be used to obtain an approximation of the actual hydrodynamic parameter 
of interest at each node in much the same manner as an estimate of the maxi- 
mum deformation of each node is obtained by modal superposition. 

To answer the first question raised in this section, the suitability 
of dropping the velocity force, [C ]{x }, from Eq. 3.40, response calculations 
were made for the following two equations of motion: 

r-Mj{x s > + [C s ]{x s > + rK DL -J{x $ } + [K]{x s > 

= [K]{x g } + [C s ]{x g } (3.40) 



75 



and 

^Mj{x s > + [C s ]{x s > + rK DL ^]{x s } + [K]{x $ } = [K]{x g } (3.50) 

The quantities {|x c l }, {<|x l>}, {|xl >, and {<|x |>} for systems 1, 

S mdX b b MldA b 

4, and 7 in the mid-frequency range were calculated for the El Centro earth- 
quake from both Eqs. 3.40 and 3.50. The damping matrices [C ] used in the 
series of calculations were such that they yielded damping ratios of .02, 
.05, and .10 in each mode and ["~K DL -J was set to zero. For each structural 
system and value of [C ], the hydrodynamic parameters computed from Eq. 3.40 
were within 5 percent of the corresponding response quantities computed from 
Eq. 3.50. The results of the calculations for system 4 and a damping matrix 
which yields .02 in each mode are shown in Table 3.34. In another set of 
calculations, the damping matrices [C ] were made to be proportional to the 

mass matrix and the numerical values of [C ] were such that the first mode 

s 

damping ratios were .02, .05, and .10. Again, for each structural system 
and value of [C ], the response quantities computed from Eq. 3.40 were within 
5 percent of the corresponding response quantities computed from Eq. 3.50. 
The numerical results were such that no clear trend resulted that indicated 
which equation yielded consistently higher or lower results. The hydrodynamic 
parameters were computed for system 4M in the mid-frequency range, with a 
structural damping matrix which yielded modal damping ratios of .02 in each 
mode, for the El Centro earthquake. The drag factor matrix was linearized by 
using the ground velocity characteristics and made to be proportional to the 
mass matrix. In one set of computations, the velocity force [C ]{x } in Eq. 
3.40 was included and in another set of computations, the velocity force 



76 



[C ]{x } was neglected. The two sets of numerical results differed by less 
s g 

than 5 percent. 

From these calculations, it is concluded that the velocity force 
[C ]{x } can be dropped from Eq. 3.40 without sacrificing the accuracy of 
the results by more than about 5 percent, for values of [C ] which yield 
modal damping ratios of up to about .10. 

In order to show the similarity of form between Eq. 3.48 and the 
linear equation of motion for the single degree of freedom oscillator dis- 
cussed in Chapter 2, it is instructive to recall Eq. 2.7, repeated here for 
convenience. 

• * o 

Z + 23 oaZ + 2B.u)Z + a) Z = -x - 23 u o)X (3.51) 

s n g h g 

Since Z = x - x , Eq. 3.51 can be written 
s g 

SL + 23 cox + 23 u cdx^ + cA = w 2 x + 23 wx (3.52) 

ssshs s gsg 

It was seen in Chapter 2 that, for values of 3 total up to about .10, the 
hydrodynamic parameters computed from Eq. 3.51 were dependent upon the amount 
of total damping in the system (3 + 3 h ) and not on the distribution of the 
damping between structural and hydraulic. If all of the damping in Eq. 3.51 
is considered to be structural and all of the damping in Eq. 3.52 is considered 
to be hydraulic, the velocity force on the right side of both equations can 
be dropped, and Eqs. 3.51 and 3.52 become 

Z + 23 t ooZ + o) 2 Z = -x (3.51a) 



and 



2 2 

x s + 23 t wx s + a) x s = (ox (3.52a) 



77 



In other words, for values of B t up to about .10, the hydrodynamic parameters 

lx » <|x |>, |x I , and <|x l> computed from Eq. 3.51a are within 2 
's'max ' s 1 ' s'max ' s 1 v ^ 

to 4 percent of those which would be computed from Eq. 3.52a for the same 
system and base disturbance. 

It is seen that Eq. 3.48 is of the same form as Eq. 3.52a, so if 
the hydrodynamic parameters can be calculated, or estimated (as from an ideal- 
ized response spectrum) for Eq. 3.52a with satisfactory accuracy, then modal 

hydrodynamic parameters Iql ,<|q|>, Iql , and <|q|> can also be calculated 
j j r '^'max Ml M, max '^' 

or estimated. Once the modal response quantities M max » <hl > » l^l max » anc ' 
<|q|> are obtained and multiplied times the appropriate modal hydrodynamic 
parameter participation factor to obtain |Q| , <|Q|>, |Q| , and <|Q|>, 

II Id A IMdA 

the problem arises of how to combine the modal responses. 

To obtain an estimate of (|x I > and {|x I ), the modal responses 

s max s max 

can be combined in any one of several methods as is the case for obtaining 

{|ZL,„K An upper bound is obtained by summing the absolute values of the 

max 

modal responses (ZABS). 

An upper bound on the quantities {<|x |>} and {<|x |>} can also be 
obtained by the EABS method of modal combination, but this is not readily 
apparent. That the ZABS method of modal combination yields an upper bound 
on the quantity {<|x |>} (or {<|x |>}) is shown as follows: 

{x s > = [<i>]{Q} (3.42) 

Assume that the vector {Q(t)> has been obtained, then, at the jth node of 
the system, 

x (t) = ♦ J1 Q 1 (t) + * j2 Q 2 (t) ♦ . . . * j;nm Q nm (t) (3.53) 



78 



Taking the absolute value of both sides of Eq. 3.53 



|x. (t) 
J 



(J^Q^t) + <J>. 2 Q 2 (t) + 



cj>. Q (t) 



(3.54) 



An upper bound on |x (t)| is seen from Eq. 3.54 to be 

J 



|x (t)| < |<fr il | IQ-, (t) | + k i2 MQ 2 (t)| + 



k iiq (t) 

1T j ,nm' |X nm v ' 



Integrating both sides of Eq. 3.55 over the time of response, 



(3.55) 



f t , f t 

|x s (t)|dt < j Cl*j-, I IQ-, (t) I + k- 2 MQ 2 (t) 



>• I IQ (t)|] dt 
v j ,nm' |X nm v ' ' J 



(3.56) 



or, 



<|x s |> < k-pMQ^ + k j2 l<|Q 2 l> 

J 



+ . . . |<J>. |<|Q |> 
Ir j,nm' ' x nm' 



(3.57) 



Which is seen to be the IABS method of modal combination. 

Rules for constructing idealized hydrodynamic parameter response 
spectra from which |q| , <|q|>, |q| » and <|q|> may be estimated for each 

• • 

mode (and then |Q| » <|Q|>» iQl •> and <|Q|> are computed from the q's and 
|N| max |X| |X| max ' ' v ^ 

the hydrodynamic parameter participation factors) of the multi-degree of 
freedom system are discussed in the next section. 



79 



3.5 Idealized Elastic Hydrodynamic Parameter Response Spectra 



Idealized elastic hydrodynamic parameter response spectra can be 
constructed for each mode of the multi -degree of freedom system in the fol- 
lowing manner: 

1. Compute the natural frequencies, ["w-J, and mode shapes, [<J>], 
for the system. 

2. Establish the structural damping ratio, 3 » for each mode. 

s i 

3. Compute 3. and HDPF. from 



a = 



nn \ 

i V. 

J = 1 JJ 
nn 

J-l MjJ / 



<x 2 |x |> \ 

g 1 g 1 

•2 
<x > 

g 



(3.22) 



r23 h w-J = aMJ 

{HDPF} = rKtj _1 [(})] T [K]{I} 



(3.24) 
(3.49) 



4. With the quantities go.., 3<-., 3 h » x 



n 



g max 



(or <|x |>), x 



g max 



(or <|x |>), and x (or <|x |>), construct the idealized 
v ' g 1 g max v ' g 

elastic hydrodynamic parameter response spectrum for the ith 
mode exactly as described in Section 2.7 for the single degree 
of freedom system. 
When an idealized spectrum has been drawn for each mode of the sys- 
tem, maximum modal hydrodynamic parameters are obtained from the spectra, 
multiplied times the appropriate modal hydrodynamic parameter participation 
factor , and combined in some manner to yield an approximate solution of the 
hydrodynamic parameter of interest. 



80 



CHAPTER 4 

APPLICATIONS 

4.1 General 

In Chapters 2 and 3 a method was developed for linearizing the non- 
linear hydrodynamic drag force on a single degree of freedom oscillator and 
a multi-degree of freedom lumped parameter model. The method has been shown 
to yield satisfactory results for systems subjected to earthquake excitation 
of the type used in this thesis. Although the method of linearizing employed 
in the multi -degree of freedom system places a linear damper at the level of 
the top mass where a nonlinear damper does not exist, it has been shown to 
yield maximum response quantities which are within a wery few percent of the 
response quantities computed for the nonlinear system. Further, linearizing 
the drag force by using velocity characteristics of the ground motion has been 
shown to yield generally conservative results in all but the low frequency 
range. The linearization technique has been developed in such a manner that 
the resulting linear simultaneous differential equations of motion for the 
multi-degree of freedom system possess classical normal modes of response. 
The existence of classical normal modes permits the use of normal mode 
superposition, with the modal response quantities determined by response 
spectrum techniques, as an approximate method of computing the response of 
multi -degree of freedom systems. The approximate method can be used for dis- 
placement response quantities and hydrodynamic parameter response quantities. 
The research reported in this thesis is not intended to reinvent the method of 
solution by the superposition of normal mode solutions as determined by 



81 



response spectra, but is devoted primarily to developing the linearizing 
technique which insures the existence of classical normal modes and yields 
generally conservative results. 

This chapter demonstrates the use of the principles and methods 
developed and discussed in Chapters 2 and 3 in computing the response of 
a series of actual offshore tower designs and one of the test systems des- 
cribed in Chapter 3. 

4.2 Displacement Response 

Table 4.1 lists the properties of a series of offshore towers de- 
signed for water depths of 400, 600, 800, and 1000 feet. 1 * A structural damp- 
ing matrix [C ] which yields modal damping ratios of .01 in each mode is com- 
puted for each tower as described in Chapter 3. The structures are subjected 
to the El Centro earthquake depicted in Fig. 1.2, and various response quan- 
tities are computed. In the first set of computations, the equations of mo- 
tion are numerically integrated and response quantities are found for the 
case in which there are no hydrodynamic drag forces acting on the structure. 
The same response quantities are next computed for the case in which the actual 
nonlinear drag forces are acting on the structure. Finally, the nonlinear 
drag forces are linearized by using the velocity characteristics of the 
ground motion, and the response quantities are computed by the combination 
(ZABS and SRSS) of maximum modal responses found from the true response spec- 
trum for each of the first five modes of the structures. The amount of linear 
hydraulic damping in each mode found from the linearization procedure is shown 
in Table 4.2. The response quantities of interest in these calculations are 



82 



the maximum displacement between the top deck and the ground, the maximum over- 
turning moment, and the maximum base shear expressed as a percent of the total 
tower weight, including the added mass of the structure. The results of the 
calculations are shown in Fig. 4.1. 

A study of Fig. 4.1 reveals that, for this series of towers sub- 
jected to the El Centro earthquake, the nonlinear hydrodynamic drag forces 
reduce the response of the tallest tower in the top deck displacement and 
overturning moment quantities by approximately 30 percent from the "no drag" 
case. The maximum base shear for the tallest tower is reduced only about 8 
percent by the nonlinear hydrodynamic drag forces. Exact response calculations 
were made for the other three earthquake records used in this thesis and the 
reduction in response due to drag was found to be somewhat lower in magnitude 
than for the El Centro earthquake. For the tower in 1000 feet of water, the 
reduction (due to hydrodynamic drag) in the maximum top deck displacement 
relative to the ground was found to be about 8.5 percent for the Taft earth- 
quake, 11.5 percent for the Ferndale earthquake, and 17 percent for the San 
Fernando earthquake. In general, the taller, more flexible towers showed 
more reduction in response due to the hydraulic drag than did the shorter, 
stiffer towers. No generalizations can be made, however, regarding the mag- 
nitude of the reduction in response relative to tower height or stiffness 
since the actual response is such a complex combination of variables in both 
the structure and the earthquake. 

In the superposition of maximum modal responses computed from the 
true response spectrum for each of the first five modes of vibration, it was 
found that the higher modes contributed rather strongly to the maximum base 



83 



shear. The contribution of each mode to the maximum base shear computed by 
the ZABS combination of modal responses is shown in Table 4.3. Although the 
SRSS combination of modal responses appears from Fig. 4.1 to provide a very 
good estimate of the response of this series of towers to the El Centro earth- 
quake, generalities concerning the accuracy of one method of modal combination 
relative to another method of modal combination cannot be made. 13 

The response of the towers is computed by the combination of maxi- 
mum modal responses (ZABS and SRSS) found from the idealized deformation re- 
sponse spectrum for each of the first five modes of vibration. The idealized 
spectra were constructed in accordance with the procedure described in Chapter 
3 for ground motion quantities equal to those of the El Centro earthquake. The 
idealized spectra for the first five modes of tower C are shown in Fig. 4.2. 
The estimated hydraulic damping ratios in the 3rd, 4th, and 5th modes of the 
structure are such that the resulting idealized spectra for those modes cannot 
be shown separately and distinctly on the scale of Fig. 4.2. It is noted that, 
for the idealized spectra shown in Fig. 4.2, the frequencies of the system are 
well removed from the high frequency tail region of their respective response 
spectrum. This was found to be the case for each of the towers A, B, C, and 
D. The results of the computations using the idealized spectra are shown in 
Fig. 4.3. 

4.3 Hydrodynamic Parameters 

To demonstrate the computation of the hydrodynamic parameters 
l x eL av > <|x l>, |x I . . and <|x l> at each node of a multi-degree of freedom 

o HldX 5 S ITlaX S 

system, the five degree of freedom system 4M is used. The properties of this 



84 



system, with a structural damping matrix that yields a damping ratio of .02 
in each mode, are shown in Table 4.4. The magnitude of [K] was chosen to 
yield frequencies of the system that fall into the velocity amplification 
region of the spectrum. The hydrodynamic parameter response quantities are 
computed by the numerical integration of the equations of motion and by the 
combination (ZABS and SRSS) of maximum modal responses found from the true 
spectral response in each mode. The results of the computations are shown 
in Table 4.5. It is seen from Table 4.5 that the combination of modal re- 
sponses provides results which are, in general, sufficiently close to the 
exact response at each node to enable the selection of inertia and drag 
coefficients C, and C n with reasonable confidence. In lieu of using the 
true spectral response quantities, which require the use of a digital com- 
puter to obtain for each mode, an idealized spectrum can be constructed for 
each mode in the manner set forth in Chapter 3. 



85 



CHAPTER 5 
CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER STUDY 
5.1 Conclusions 

In this thesis, an approximate method has been developed for com- 
puting the response of a multi-degree of freedom system, partially submerged 
in water, to earthquake excitation. In Chapter 2, the effects of the non- 
linear hydrodynamic drag force on a single degree of freedom oscillator are 
shown, and a generally conservative method of linearizing the drag force is 
developed. Amplification factors are developed which permit the construction 
of idealized response spectra for deformation and hydrodynamic parameters. 
Chapter 3 extends the principles from the single degree of freedom oscillator 
to multi-degree of freedom systems and develops a generally conservative 
method of linearizing the drag forces. The method of linearizing insures the 
existence of classical normal modes in the equations of motion, which in turn 
permits the response quantities of interest to be obtained by the superposition 
of normal mode responses. In Chapter 4 the response to the El Centro earthquake 
of a series of offshore towers is computed using the methods developed in 
Chapter 3. 

Several conclusions may be drawn from the development of principles 
and methods and the results of sample problems in the preceding three chapters. 

1. The maximum relative displacement response of a single degree 

of freedom oscillator, with drag characteristics described by 

K x 
the parameter 9 max , approaches a constant value at high 

frequencies as a result of the nonlinear hydrodynamic drag 



86 



force growing very large relative to the inertia force in the 
equation of motion. The magnitude of this relatively constant 
high frequency tail can be estimated for earthquake motions by 
the expression 



' K, x ' * 2 



'max 



D g max 
K 



/ x- 
g max 

x g max 



2. Linearizing the drag force on a single degree of freedom oscil- 
lator by using the absolute velocity response of the oscillator 
yields slightly conservative results for the maximum response 
to earthquake motions until the high frequency, high drag tail 
begins. 

3. Linearizing the drag force on a single degree of freedom oscil- 
lator by using the velocity characteristics of the ground motion 
yields conservative results for the maximum response to earth- 
quake motions except for low frequency systems and very high 
frequency systems. 

4. The conservatism introduced by using the ground motion velocity 
characteristics in the linearization of the drag force is re- 
duced as the amount of structural damping in the system is in- 
creased. 

5. The maximum response of the single degree of freedom oscillator 
to earthquake motions is sensitive to the total amount of linear, 
velocity dependent damping in the system, and not to the distri- 
bution of this damping between structural and hydraulic, up to 
linear hydraulic damping ratios of 10 percent of critical. 



87 



6. The nonlinear hydrodynamic drag has \/ery little effect on the 
elasto-plastic deformation response spectrum in the low fre- 
quency region. 

7. A high frequency tail exists in the elasto-plastic deformation 
response spectrum for a system with nonlinear hydrodynamic drag 
forces. Large amounts of drag cause greater reductions in the 
yield deformation, Z , from the maximum elastic deformation for 
a given ductility factor than do small amounts of drag. 

8. The nonlinear hydrodynamic drag force has a damping effect on 
the elasto-plastic deformation response spectrum in the mid- 
frequency range. The damping effect of the drag becomes less 
pronounced as the ductility factor increases. 

9. Idealized response spectra which consider the effects of fluid- 
structure interaction can be constructed as described in this 
thesis. 

10. The linearization of the drag forces on a multi -degree of freedom 
system by using the absolute velocity response at each node and 
forcing the linear drag factor matrix [^IC..^] to be proportional 
to the mass matrix ["Mj as described herein is satisfactory. 

11. Linearizing the drag forces on a multi-degree of freedom system 
by using the velocity characteristics of the ground motion and 
forcing the drag factor matrix to be proportional to the mass 
matrix as described herein yields generally conservative results 
except for low frequency systems. 

12. For the multi-degree of freedom systems studied in this thesis, 



88 



the response to earthquake excitation is relatively insensitive 
to the spatial distribution of the linear drag forces. 

13. The hydrodynamic drag forces can cause a significant reduction 
in the response of lightly damped systems to earthquake motions 

14. The amount of reduction in response due to hydrodynamic drag 
varies considerably from one response quantity to another and 
from one earthquake to another. 

15. The reduction in response due to hydrodynamic drag is decreased 
as the amount of structural damping in the system is increased. 

16. Higher modes of a multi-degree of freedom system can contribute 
appreciably to the total response of the system. 

5.2 Recommendations for Further Study 

The approximate methods of analysis developed in this thesis are 
limited by the types of multi -degree of freedom systems used in the investi- 
gation and by the inherent limitations in the hydrodynamic force equation 
used. Further, the study in this thesis is devoted to excitation of the 
structure in still water, and the ocean is never completely at rest. There 
are several areas in which further studies should be made of the response of 
offshore structures to earthquake excitation. 

1. The validity of the lumped parameter model should be tested 
through the use of field measurements of the response of actual 
offshore structures to strong motion earthquakes. 

2. Model tests of single degree of freedom oscillators and multi- 
degree of freedom structures should be conducted for the types 



89 



of base motion considered in this thesis. Such model tests will 
be useful in verifying the principles developed herein. 

3. Since the ocean is never actually at rest, analytical and ex- 
perimental studies should be conducted on the response of sub- 
merged and partially submerged structures subjected to earthquake 
motions combined with forces resulting from waves and currents. 

4. The studies in this thesis assume ground motion in one direction 
only. It is recommended that studies be made of the response 
when the two orthogonal components of the horizontal ground motion 
are acting on the structure at the same time. 

5. The earthquake response of the structure in torsion and in the 
vertical direction should be investigated. 

6. It is recommended that the effects of foundation and soil con- 
ditions be included in the model. There are several reasonable 
approaches to modeling the foundation which should be investi- 
gated. 23 " 25 

7. The hydrodynamic force equation used in this thesis (Morison's 
equation) is based on studies with relatively rigid piles. There 
is some evidence 19 ' 20 that the forces on flexible, oscillating 
structures may be better expressed through the use of different 
drag and inertia coefficients, or even through the use of a 
different force expression. Much more information is needed 
concerning the hydrodynamic forces acting on flexible, oscillating 
structures. 

8. The linearizing technique should be tested for suitability of 



90 



use when the structure has radically different distribution of 
mass, stiffness, and drag properties from those test structures 
used in this thesis. 
9. It is recommended that the effects of the hydrodynamic forces 
on the inelastic response of the structure be studied in greater 
depth. While design for elastic response is satisfactory for 
earthquakes which may be expected to occur frequently, elastic 
design for infrequent, severe earthquakes may result in ex- 
cessively conservative designs. Some response into the in- 
elastic range should be permitted for the occurrence of an un- 
usually strong earthquake, and approximate methods are desirable 
for the estimation of this inelastic response. 
10. It is recommended that approximate methods be developed for 
the estimation of the response to stochastic representations 
of the forces resulting from earthquakes, waves, and currents. 



91 



LIST OF REFERENCES 

1. Hurty, W. C. and Rubinstein, M. F., Dynamics of Structures , Prentice- 
Hall, Englewood Cliffs, New Jersey, 1965. 

2. Morison, J. R., O'Brien, M. P., Johnson, J. W. , and Schaaf, S. A., 
"The Force Exerted by Surface Waves on Piles," Petroleum Transactions, 
American Institute of Mining, Metallurgical and Petroleum Engineers, 
Vol. 189, 1950. 

3. Murtha, J. P., "The Virtual Mass of Cylindrical Bodies at a Free Surface," 
Proceedings of the Fifth Midwestern Conference on Fluid Mechanics, Uni- 
versity of Michigan Engineering Research Institute, Ann Arbor, Michigan, 
1957. 

4. Burke, B. G. and Tighe, J. T. , "A Time Series Model for Dynamic Be- 
havior of Offshore Structures," Preprints, 1971 Offshore Technology 
Conference, Vol. 1, Paper No. OTC 1403, 1971. 

5. Newmark, N. M. , "A Method of Computation for Structural Dynamics," 
Journal of the Engineering Mechanics Division, American Society of 
Civil Engineers, Vol. 85, EM3, July 1959. 

6. Malhotra, A. K. and Penzien, J., "Response of Offshore Towers to Earth- 
quake Excitation," Proceedings, Civil Engineering in the Oceans II, 
American Society of Civil Engineers Conference, Miami Beach, Florida, 
1969. 

7. Penzien, J., Kaul, M. K. , and Berge, B., "Stochastic Response of Off- 
shore Towers," National Symposium on Computerized Structural Analysis 
and Design, George Washington University, Washington, D. C, March 1972. 

8. Malhotra, A. K. and Penzien, J., "Response of Offshore Structures to 
Random Wave Forces," Journal of the Structural Division, American Society 
of Civil Engineers, Vol. 96, ST10, October 1970. 

9. Foster, E. T. , Jr., "Statistical Prediction of Wave Induced Responses 

in Deep Ocean Tower Structures," Ph.D. Thesis, University of California, 
Berkeley, 1967. 

10. Nath, J. H. and Harleman, D.R.F., "The Dynamics of Fixed Towers in 
Deep Water Random Waves," Proceedings, Civil Engineering in the Oceans, 
American Society of Civil Engineers Conference, San Francisco, 1967. 

11. Blume, J. A., Newmark, N. M., and Corning L. H., Design of Multistory 
Reinforced Concrete Buildings for Earthquake Motions , Portland Cement 
Association, Chicago, 1961. 



92 



12. Wiegel, R. L., Editor, Earthquake Engineering , Prentice-Hall, Englewood 
Cliffs, New Jersey, 1970. 

13. Newmark, N. M. , et al., "Design Procedures for Shock Isolation Systems 
of Underground Protective Structures," Report RTD-TDR-63-3096, Air Force 
Weapons Laboratory, Albuquerque, New Mexico, Vol. 3, 1964, and Vol. 5, 
1965. 

14. Newmark, N. M. and Rosenblueth, E., Fundamentals of Earthquake Engineering , 
Prentice-Hall, Englewood Cliffs, New Jersey, 1971. 

15. Jacobsen, L. S. and Ayre, R. S., Engineering Vibrations , McGraw-Hill, 
New York, 1958. 

16. Amin, M. , "A Non-Stationary Stochastic Model for Strong Motion Earth- 
quakes," Ph.D. Thesis, University of Illinois, Urbana, Illinois, 1966. 

17. Ippen, A. T. , Editor, Estuary and Coastline Hydrodynamics , McGraw-Hill, 
New York, 1966. 

18. Wiegel, R. L., Oceanographical Engineering , Prentice-Hall, Englewood 
Cliffs, New Jersey, 1964. 

19. Keulegan, G. H. and Carpenter, L. H., "Forces on Cylinders and Plates 
in an Oscillating Fluid," Journal of Research, National Bureau of 
Standards, Vol. 60, No. 5, May 1958. 

20. Laird, A.D.K., "Water Forces on Flexible Oscillating Cylinders," 
Journal of the Waterways and Harbors Division, American Society of 
Civil Engineers, Vol. 88, WW3, August 1962. 

21. Caughey, T. K. , "Classical Normal Modes in Damped Linear Dynamic Systems," 
Journal of Applied Mechanics, Vol. 27, June 1960. 

22. Kassawara, R. P., "Earthquake Response of Light Multiple Degree of 
Freedom Secondary Systems by Spectrum Techniques," Ph.D. Thesis, Uni- 
versity of Illinois, Urbana, Illinois, 1970. 

23. Saul, W. E., "Static and Dynamic Analysis of Pile Foundations," Journal 
of the Structural Division, American Society of Civil Engineers, Vol. 94, 
ST5, May 1968. 

24. Davisson, M. T. and Robinson, K. E., "Bending and Buckling of Partially 
Embedded Piles," Proceedings, Sixth International Conference on Soil 
Mechanics and Foundation Engineering, Toronto, Canada, 1965. 

25. Ross, H. E., "Dynamic Response of Offshore Piling," Preprints, 1971 Off- 
shore Technology Conference, Vol. II, Paper No. 0TC 1480, 1971. 



93 




x 

rC 

E 
cd 



•x 



CD 



O 

e 



A 




(_> 















CD 


co 


i — 


CO 


*d- 


cn 




CO 


co 


o 


^1- 


CNJ 


• x 


A 


^^ 


i — 


co 


cd 


cd 


— 


C\J CD 


• 


• 


• 


• 


• 


cm en 


• X 


e 


CO 


CM 


r-» 


C\J 


•X 


V 


•i — 




CM 






V 




" — ' 











■a 

CD 
CO 



co 

CD 

ra 

3 

cr 

.e 
+J 

s- 

05 

LU 



O 

E E 
O O 

'I — T— 

+-> 4-> 
fO O 

s- s: 

Q 



X 

rO 



O 
CD 
CO 



CD 4- 

r— O 



rC 



CO 

a 

•r- 
-M 
CO 
•r— 

S- 
CD 
+-> 
O 
rC 

s- 

rO 



X 

rC 



CD 



X 

re 

E 

CD 



a 

QJ 
co 



CD 



X 



CD 
E 
ra 



C\J 
CO 

<3- 



o 

LO 

o 



*3- 

CO 
LO 



1^ 
*3- 



o 

CM 



CO 



•3- 

CM 



CO 



CD 



CNJ 



CO 
CD* 



CO 



CO 
CM 



o 



CO 



co 



o 

CO 



o 

CO 



o 

«3-' 



co 



CD 
CM 



o 

CO 



CO 



CM 
CO 

o 



CM 



CO 



CM 
CO 



CO 



o 




n 










*3- 




-a 




-^- 






CD 




•> S- 




LO 






p ~ 




f0 o 

•i- cj 




CD 






r» 




C CD 








CM 


rC 




S- C£ 




ft 




LO 


•i— 




O 




ra 




CD 


e 




4- E 




• r— 




i^ 


i~ 




•r- rd 


+-> 


E 


+-> 


+-> 


o 




r— Q 


e 


s- 


e 


« E 


4- 




fO 


CD 


o 


CD 


ra CD 


•!"■ 


+-> 


C_3 re 


e 


4- 


E 


•i- E 


1— 


E 


E 


o 


•1— 


o 


E O 


ra 


CD 


n .|— 


Q. 


1 — 


Q. 


s- a. 


o 


E 


O O 


E 


ra 


E 


O E 




o 


-o a 


o 


o 


O 


4- O 


r- 


o_ 


e re 


o 




c_> 


•r- O 


o 


E 


ro Q_ 




ft 




1 — 


s- 


o 


c 


L±J 


CD 


LU 


ra LU 


+-> 


c_> 


i- « 


1 


r— 


1 


C_) 1 


E 




a> i— 


CO 


ra 


^J- 


r— 


CD 


oo 


Li_ |-^ 


n— 


"O 


-=3" 


*>CM 


C_3 


1 


CD 


1 


E 


1 


■»-> 1 




z 


E i— 


co 


t- 


Z 


4- z: 


i— 




ra 




O) 




ra 


LU 




CO 




U- 




1— 



94 



-o 

3 



+-> 

c 
o 
o 



<u 






A 


X-— > 




ns CD 


Cn 


E c 


X 


O 




cn c 


V 


:x — - 



A 


x^-> 




ra a> 


CD 


E c 


X 


o 




cn c: 


V 


•x — - 



A 


X 






to 


a> 


CD 


E 


E 


X 




O 




CT> 


c 


V 


X 





A 


T— 


r-^ 


wo 


CTi 





r^ 


CO 


-3- 


C\J 


OV — » 


LO 


o 


CM 


CO 


:x en 


o 


i— 


o 


o 



V T- 



E 



CO 
00 



wo 



oo 

CO 

o 



CM 



00 

o 



*3- 

CM 



LO 
r— 
CvJ 

O 






co 



CX> 



LO 
00 



O 
WO 



LO 
00 
CO 



u 










a a> 


o 


r-. 


WO 


*d- 


10 


^1- 


CM 


p— 


cr> 


cn^ 


r— 


«3- 


O 


cr> 


X 


• 


-• 


• 


• 


— c 


CVJ 


LO 


CM 


o 



— 


co 


CO 


CO 


o 


en c: 


CVJ 


cn 


i^ 


r>. 


X 'r- 


wo 


CTl 


LO 


CVJ 



o 


#\ 










<3- 


-o 




«3- 






CT> 


« s_ 




LO 






r ~ 


03 O 

■r- O 




CTl 






#* 


C CD 








CM 


03 


s_ a: 




#1 




LO 


•r— 


o 




03 




CT> 


c 


M- E 




•i — 




■ — 


s- 


•■- 03 


+-> 


c 


+-> 


+J 


o 


r— Q 


c 


t- 


c 


* C 


4- 


fO 


cu 


o 


CD 


03 CO 


•r- 4-> 


C_) 03 


c 


4- 


C 


•r- E 


i — C 


E 


o 


■r«" 


o 


E O 


03 0J 


*» *F™ 


Q. 


i^ 


D_ 


S- CL 


O C 


o o 


E 


<d 


E 


O E 


o 


"0 O 


O 


O 


o 


4- O 


•> Q- 


C (T3 


o 




c_> 


•r- O 


O E 


03 Q_ 




rt 




■ — 


S- o 


E 


LU 


CD 


LU 


03 LU 


+-> o 


S- *> 


1 


i^ 


1 


O 1 


c 


CD -— 


WD 


03 «* 


r~— 


CU 00 


u_ r-~ 


r— 


-a <t 


«CM 


O 1 


CX> 


1 


E 


1 


+-> 1 


z 


c ■ — 


OO 


S- 


Z 


4- Z 


r— 


fO 




a> 




03 


LU 


oo 




u_ 




1— 



95 



Table 2.1 



Characteristics of Series Representation 
of Base Acceleration 



Quantity Maximum Amplitude Time of Occurrence 
x 2.56 g 0.35 t. 

g d 

x 3.85 ft/sec 0.42 t, 

9 d 

x 0.20 ft 0.50 t, 

9 d 

x = -0.20401 cos 2-rrt - 6.87108 cos 4iTt + 38.35016 cos 6TTt 

g 

- 41.35223 cos 8-rrt - 2.84232 cos lOirt 
+ 12.91937 cos 12-irt 

(x in ft/sec 2 ) 
y 



96 





n3 






■o 






CU 






+J 






3 


c 




Q- 


o 




E 


•r— 




O 


+-> 




<_> 


to 




X 


o> 




fO 


cu 




E 


+-> 







c 




M 


1— 1 




-C 


fO 




+-> 


(J 




"r— 


•^ 


C\J 


3 


s- 


• 




<u 


CM 


X 


E 




(0 


3 


CD 


E 


z: 


^— 


■ 




-Q 


r-j 


>> 


CO 


— 


-Q 


1— 








"D 


to 




CU 


CU 




+J 


•^ 




<TJ 


o 




E 


c 




•r" 


<L) 




■M 


15 




CO 


cr 




UJ 


cu 




<4- 


u_ 




O 


.c 




c 


en 




o 


•r- 




to 


IE 




•^- 






s- 






fO 






Q- 






E 






O 






o 





o 

•r- 

S- 
cn 
cu 
+-> 

c 



fO 

o 

•r- S- 

s- o 
cu u. 

E 

3 i— 

z • 

CM 

E 

o • 
s- cr 



to o 

cu 

JZ 
o 

c 



X 

fO 



M 



o 



o 
II 



to 



oa 



CM 
O 



o 

II 



oa 



o 
o 
II 

to 

oa 



o 
o 

o 

II 

ca 



00 

cu 



o 



E cr 



O <3" 

c -a • 

•r- cu CM 
- — 4-> 

X 

fO T- 

E 4-> 

to 

M LU 



:x 






cn ^ 



>> 




u 




c 




cu 


00 


Z5 


D_ 


cr 


o 


O) 




S- 





cu 
(J 

c 

fO 

cu J2 
oo s- 

(O =3 

DQ +J 

OO 



r>~ 


CO 


LO 


CO 


00 


lo 


r- 


to 


LO 


tO 


cn 


CM 


O 


00 


1 — 



CT< 
O 
CM 
tD 
O 



CM 



cn 
cn 
cn 

CO 



to 
o 
co 



CM 



^1- 


to 


Cn 


CTl 


r^ 


CM 


00 


00 


to 


"vT 


r->» 


CO 


O 


CT> 


cn 



CM 



O O 



LT) 





c 




o 


r— ■ 


■r" 


ra 


+-> 


T3 


fT3 


• 1 — 


S- 


o 


O) 


00 


( — 


Z5 


cu 


c 


o 


•r— 


<_> 


CO «=C 



CO 

*3- 



•3- 
o 



*d- 


^1- 


00 


o 


co 


r— 


o 


r*» 


to 


r^ 


CM 


CO 


o 


i — 


to 



LO i — tO 

o <3- r^ 

o r-» to 

i— CM CO 

o r— to 



LT) 

to 

CO 

o 



r*^ 


CO 


«d- 


o 


<d- 


^~ 


o 


r^ 


r^ 


i i— 


CM 


CO 


1 o 


i — 


to 



to 

LO 



CO 

<3- 



CM 


, — 


CO 


r>. 


cn 


to 


cn 


cn 


r^ 


o 


CM 


r~~ 


o 


i — 


to 











to 






r— 


o 


O 


O 


O 


00 


o 


o 


CM 


to 


CM 


O 


o 


LO 



o 

CM 



o o o 

CO CO i — 



to 




CU 




•P" 




s_ 


cu 


cu 


O -* 


E CO 


S_ fO 


s- 


+-> zs 


cu cu 


c cr 


I— c 


cu -c 


•r— 


O +J 


X 00 


s_ 


•i- o 


«— fO 


CO c_> 


LU UJ 



97 



Table 2.3 

Distribution of Total Damping Between Structural 
and Hydraulic for Comparison Purposes 









B h For 






B total 


3 s = 


3 s 


= .02 


3 S = .05 


3 = .10 

s 


.02 


.02 











.05 


.05 











.07 






.05 


.02 




.10 


.10 






.05 





.12 






.10 




.02 


.15 








.10 


.05 



Table 2.4 
Elastic Deformation Spectrum Amplification Factors 







Ampl- 


ification 


Factor 




e total^ 


Displacement 


Velocity 


Acceleration 





2.5 




4.0 




6.4 


0.5 


2.2 




3.6 




5.8 


1 


2.0 




3.2 




5.2 


2 


1.8 




2.8 




4.3 


5 


1.4 




1.9 




2.6 


7 


1.2 




1.5 




1.9 


10 


1.1 




1.3 




1.5 


20 


1.0 




1.1 




1.2 



98 



Table 2.5 

Elastic Hydrodynamic Parameter Spectrum 
Amplification Factors 



IxJ Spectrum 
1 s'max K 

Amplification Factors 

total Displacement Velocity 

(%) 



2.4 5.2 

1 2.2 4.4 

2 2.1 3.6 
5 1.8 3.1 

10 1.6 2.1 



<|x |> Spectrum 

Amplification Factors 

total Displacement Velocity 

(%) 



3.8 10.9 

1 3.4 8.5 

2 3.0 6.8 
5 2.3 4.2 

10 1.8 3.3 



99 



Table 2.5 (Continued) 







• • 

1 s 
Ampli 


Lax s P ect ™m 
fication Factors 




3 total 
(%) 


Displacement 


Veloci 


ty 


Acceleration 





2.2 




4.1 






7.1 


1 


1.9 




3.1 






4.9 


2 


1.6 




2.6 






3.7 


5 


1.4 




2.0 






3.1 


10 


1.2 




1.8 






2.6 



<|x |> Spectrum 
Amplification Factors 
total Displacement Velocity Acceleration 






3.4 


10.1 


13.5 


1 


3.0 


6.3 


6.2 


2 


2.7 


5.1 


4.3 


5 


2.1 


3.0 


2.9 


10 


1.6 


2.2 


2.2 



100 



Table 2.6 



Actual and Approximate Reduction Factors for the 
High Frequency Region of Inelastic Response 
Spectra. El Centro Earthquake 
K„x 







P s " u.. 


K 


- U. JU 












Actual 




Ductility 

y 


Factor 


Z 

y 

(inches) 


' 'max 
(inches) 


Reduction Factor 
forZ y 


y 


2y - 1 


1 




0.63676 


0.63676 


1.00 


1.00 


1.5 




0.49526 


0.74289 


0.77 


0.75 


2 




0.42835 


0.85670 


0.67 


0.67 


3 




0.35975 


1.07925 


0.56 


0.60 


4 




0.31523 


1.26093 


0.49 


0.57 



Note: All calculations are at a frequency of 10 cps. 



101 



ro 



-Q 
r<3 



CO 

E 
QJ 
4-> 
10 
>> 
00 



o 
-o 
a; 

cv 



<4- 

o 
a) 

CD 
S_ 

a> 

Q 
LT) 

s- 
o 



s- 
o 

-M 
(J 

CO 



CJ) 
03 

s- 

Q 

■o 

C 



to 

CO 

c 



00 



co 
co 
fO 



4- 
o 



CO 



CCS 



CD 

> 






a> 
a: 



r^ 


Q 

Q 


1 

1 

2 1 1 
1 

3 1 2 
1 

4 2 3 
1 

5 3 4 

.004 .008 

1.00000 
2.58720 
3.93241 
5.06643 
7.01497 

0.03036 


in 


o 


00 


O 1 — CM CO «*• O 

O cr> <*• •— 00 

O CM CM t— ct> in 

*»• cr> r» 1 — 10 

_ co in co co «s- 

.— 1— cm co o«3-mco«*0 

■ — cm co «* in 

1 — 1 — CMCMCOCM^J-CMincO 


Lf) 


a: -* 


CO 
_ O O «3- <— c~» r^ in 
• — cm co *3- r-~ co O in in 

•— i~~ •— 1— 
CO CM co r-^ «3- 
co 00 cm <y> 

' — 1— 1 — 1 — 1 — 1 — CMi — COi — , — CM CO in CO 


<d" 


a 

3: -^ 

o 

Q 


CO 

•— cm co «r 

_ O 

Or— r— CM CO O O CX> CM CO r~. ■— 

00 co 1— 
■d- co ■ — co 
in r— in in 

O CM «*■ CO 1 — 

_ r— cm co «s- in 

O r— r- 1— 1— 

r— r— r— CM 1 — CMCMCMCOCO 


co 


Q 


O r-~ r«. O cm ^- 

CM O CM O CO CO CM 

_ oincoinoocM 
<—> 1 — 1 — 1 — >— 01 — r-. in i— 1 — 

O r— CM CM «*• O 

1 — cm cm ^r in 

1— 1 — r— CMr— CMCMCOCOin 


CM 


a 



_ 

O 1— 1 — CM CO O 

O •— r^ co r-» in 

O co r-*. r-- in in 

O co co «*■ 00 

cm cm in co r-. r-~ 

_ r-. r-» in r^ 

«— cm *3- in r«» 

CM r— r— CM r— CM 1 — CM' — CO 


- 



2: ^ 

a 

_l -* 


*3" 
_ O 
O r— r— CM CO O 

CM O r— O r— lO CM 
_. O OCOi — COCMO 
Or— r— r— r— O O O «* CO ** in 

O in co 00 
r^ in **■ co 

• — cm ^- in co 

CMr— — CMr-CMr— COr— LO »>■ ~W W MJ W 



r— r— cMCMcoco^^i-inin 
£-* E -* B ■*£ B -* E .*: 



>> 
00 



o 




- — * 


ro 




!_ 


1 


3 


</> 


••-» >> 


at 


rg 


xz 


z: c: 


CJ 


0) 


c 


CD 3 


,p ~ 


> cr 


* — * 


•r- CD 




*-> i_ 


E 


ro U- 


t-J 


r— 




ai 


**■ 


ec 


O 




J* 




c~a 





r— CM CO ^T Lf 
t- «4- «♦- «4- «*- 




102 



-J c 



< a 

U 5 

Z <i 

•~ c 



r- •-< ao cm r- 

CT- CM O •■' CT 

c\ <v p- in ci 

<«"' — c o o 

o c o c o 

• • • • • 

o o o c © 



.Jf .» CM CV vT 

on .c a r- -1- 

•O ro P- IT ^ 

r ■ .-. © O c> 

o c c o o 

• t • • • 

o o c o c 



f- r- in cm 03 

(r -4 a >o «l 

f. — o o o 

o o o o o 

o o o o o 

• • t • • 

c o o o o 



r- -t m a- (v 

*c or so -• c 

f- r> ph — o 

o o c o o 

c o c o o 

• • • • • 

c o c © o 



ir g »i o or 

c o o o c 

c o c o c 

o o c o c 

• • • p • 

© o © o o 



cm a , M -L cm 

C ri rv r-' r-» 

— O © O C 

O o C © O 

c o c o c 

t • • • • 

o © c © © 





• _ 


ir. ro o •* m 


in O or. <o .» 


■* <v rr, c a 


_l 


C? m 


p- C. >i in c 


O —• r- ir in 


in ^ f f\w— 


< 


u a 


O O «. r- h 


r- P- CT- O —. 


, i ^ cr- p- o- 


c 


a. U 


cm ac ro ep .t 


>*•£>* O- in 


OilM xL- -O 


a 


u- «» 


O O •" —> CM 


(NJ sO H IA O 


m O <G -4 





-p-» 




C 




CD 




C 




o 




a. 




E 




O 




O 




00 




1 

21 




•* l™~ 




o o 




>=T • 




en 




r— II 




« <j 




CD 00. 




JXL 




fO 




3 • 




cr c 




-C o 




+-> T- 


C\J 


s- +-> 


• 


CO 3 


CO 


LiJ i — 




o 


CD 


o oo 


r— 


s_ 


-O 


-M c 


rO 


c o 


r— 


CD -r- 




C_) -M 




fO 




r— S- 




uj en 




CD 




o -t-> 




+-> E 




p— 1 




_1 




r— 4-> 




o 




E CD 




CD S_ 




-M -r- 




00 Q 




>> 




oo 




<*- 




o 




CD 




(/) 




c 




o 




a. 




(/) 




CD 




CC 



o o o o o 



c c, 
o z 

X 



•— cm ro »J in 



O -i © © -. 



t-^ r\j f vt in 



*v 


or 


p- 


ri en 


in 


r* 


o 


1" 


<»■ 


n 


<t 


•^ p- 


r\i 


u> 


rv 


r\j 


O 


P- 


CO p- 


vf 


f~ 


4 


or 


o 


a- 


r- 


•-< O 


m 


cv 


(NJ 






rp 


oc CT> 


a 


*-< 


cm 


-c 


a 


■-H 


<\j 


*C rsj 


r i 


fT| 


-* 


Uj 


_j 


a 


O a 


rr 


o 


C 


o 


•-* 


ir 


r» 


r-< ^.- 


»— i 


r ■ 


.-H 


in 


<i 


ct- 


o o 


a 


o 


c 


o 


o 


c 


O 


o o 


o 


o 


O 



o 


>v 


< 


* 


o 


IT, 


a 


<c 


Osl 


n 


o 


•o 


•* 


o 


<f 


-o 


~c 


^ 


»- 


l^> 


•— * 


CC 


r- 


OD 


r- 


r* 


<o 


— t 


-0 


r^ 


■* 


r»i 


© 


in 


O.I 


•o 


CT- 




?■ z 




o 


o- 


in 


0" 


.-> 


o 


r- 


r^ 


O 


m 


in 


f* 


Of 


t> 


c 


w-4 


o 


o c 


Uj 




o 


o 


<T 


o- 


© 


00 


CO 


u^ 


w 


p^ 


o 


a- 


CI 


o 


o 


u 


1/1 •_! 


l/> 


_J 


a 


c 


a- 


o 


o 


a 


a- 


CT. 


C 


O 


c 


a 


a 


© 


o 


m 


— ►— 


< 


< 


• 


• 


• 


1 


» 


• 


i 


t 


t 


• 


• 


• 


■ 


• 


• 


3 


a 3 


l_) 


3 


o 


r-» 


o 


o 


»-* 


o 


c 


O 


—* 


PH 


r-* 


c 


o 


,-i 


■H 




< -j 




t- 
































in 


a o 




o 
































•— i 


X i^ 




< 


































c 


^ 


































T 




o 




o 


~+ 


a 


ffl 


>1 


•c 


vT 


r~* 


r- 


>* 


p- 


(NJ 


(\i 


CO 


<\J 


ai 




< 


o 


o 


U> 


a 


-t 


in 


fM 





-J 


co 


r~ 


or 


If. 


o 


CC 


in 


_i 




CC 


< 


o 


0> 


o- 


o 


-o 


t-i 


c\ 


in 


rv 


o 


p- 


J 


J 


st 


»t 


CC 




o 


QC 


o 


o 


cr 


^H 


-» 


00 


r» 


o 


p» 


in 


in 


vC 


-f 


~o 


<o 


c 






o 


o 


o- 


o 


a 


o- 


<T> 


a 


a 


rr 


o 


cr 


CT 


CT 


CT 


a 


cc 




_l 




• 


• 


• 


• 


• 


• 


i 


• 


• 


• 


• 


• 


• 


• 


• 


a 




< 


a 


•-< 


o o 


o 


© 


o 


o 


o 


o 


o 


o 


O 


© 


o 


o 






3 


z 
































o 




K 


































< 







































4 


UJ 








in 


o 


© 


CO 


*m 


» 


IT 


ffi 


-t 


CM 


CM 


-t 


»— 


INI 


* 


3 


X 






CM 


00 


o 


CT- 


o 


© 


t-< 


Psl 


•4. 


* 


CO 


-O 


CN. 


r~. 


tr 


in 


p- 


r- 


z 






.— i 


~0 


^1" 


in 


O 


ao 


CT 


P- 


o 


fO 


p-i 


CT- 


CC 


— * 


ro 


O 




w 




UI 


>* 


pv 


rr\ 


ro 


m 


o 


r\j 


o 


rv. 


■O 


CT- 


CT- 


in 


fM 


p- 


4 


UJ 


Ui 


o 


t/1 


PO 


rv, 


pn 


cr 


r- 


o 


ph 


rr- 


^-« 


^) 


P- 


O 


© 


p- 


-c 




NJ 


X 


< 


« 


• 


• 


• 


# 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


Z 


*— t 


p- 


CC 


<_> 


00 


o 


00 


CT 


nO 


«*• 


O 


r- 


-c 


m 


m 


<r 


ro 


W-* 


o 


1-4 


OC 


LU 


o 






•— » 








p^l 


r-* 




















4 


00 




































c 


UJ 


«• 


CC 


































UJ 


z 


r- «n 


< 




CM 


ir 


•0 


O* 


>0 


co 


IT. 


-r 


INI 


eo 


ro 


>» 


P- 


m 


00 


t- 


*— 


Z UJ 


UJ 


P-4 


o 


PM 


<j 


>C 


CT- 


o 


•— • 


CT 


-O 


o 


in 


>1 


v(J 


-4- 


C) 


3 


«J 


Uj X 


z 




Wmt 


in 


-* 


i— ' 


00 


•* 


>0 


O 


« 


c< 


in 


<f 


OO 


O 


in 


a. 




s« 


•— 


UJ 


■» 


o 


ro 


O 


PvJ 


r- 


rr, 


CO 


CT 


O 


O 


-f 


•-« 


o 


MS 


X 


o 


_l 


</l 


PPl 


*-i 


ro 


P- 


P- 


•* 


CT- 


CM 


OC 


o 


p- 


o 


o 


p- 


■c 


c 


p- 


o ►- 




« 


• 


• 


• 


• 


• 


• 


• 


« 


• 


• 


• 


• 


t 


• 


• 


o 




< w 




«_> 


on 


© 


CO 


CT 


•o 


>»• 


CT- 


P- 


in 


ro 


m 


<r 


ro 


•-I 


o 




o 


_J 








*-4 








r* 






















UJ 


a. o 




































to 


</) 


oo Z 




































<>0 


_> 


— 3 






© 


>0 


in 


p- 


o 


CP 


m 


ro 


O 


in 


CM 


in 


O 


r-* 


o 


4 




Q O 


_J 




00 


~J 


p- 


-* 


■* 


Cr 


m 


P- 


ro 


4J 


ao 


ri 


CT 


r. 


*-t 


X 


l>0 


tx 


< 


o 


ۥ> 


■a 


-n 


O 


* 


«M 


o 


»— < 


CO 


p- 


CP 


O 


O 


CT- 


•* 




•— 


UJ c 


3 


< 


>r 


m 


m 


.* 


CM 


<c 


v0 


•Q 


r-4 


<!• 


tr 


u> 


CM 


CT 


•G 


X 




> 


p- 


ec 


m 


^h 


PO 


CC 


P- 


<o 


o 


^D 


CO 


in 


•c 


o 


O 


•C 


■o 


u 


> 


— o 


«_i 


i_i 


• 


• 


t 


• 


• 


• 


1 


t 


• 


• 


• 


t 


t 


• 


• 


4 


r— 


t- z 


< 




CO 


o 


CO 


cr 


•O 


•r 


o 


P- 


in 


ro 


u 


vT 


in 


r-t 


o 


UI 


P4 


< < 








•-* 








•-4 


w-i 




















O 


_ 1 




































li- 


o 


UJ (/I 




































en 


_J 


CC 1/1 






-0 


IT, 


CM 


CM 


sO 


a 


r— 


•— » 


ro 


p- 


«» 


m 


m 


-O 


w 




UJ 


< 






p- 


CT 


00 


•c 


IM 


Cr 


ro 


CM 


-o 


^ > 


in 


CM 


r- 


^^ 


in 


> 


> 


X X 




o 


rr. 


•» 


-n 


cr 


•*■ 


CM 


O 


CM 


ro 


^-4 


o 


O 


o 


.--4 


00 


»- 




3 


r^ 


4 


^■ 


<* 


rr- 


o 


© 


«!■ 


-* 


<0 


p- 


m 


in 


o 


ro 


-n 


ar 


t_a 


o 


X 


Z 


CC 


fO 


^^ 


m 


oc 


t-< 


cr 


fO 


<f 


m 


r- 


CT- 


r-j 


r-H 


p 


•C 


u 


z 


** 




o 


• 


• 


• 


• 


• 


• 


• 


• 


t 


• 


• 


• 


« 


• 


• 


o 


3 


X 






00 


p>I 


00 


o 


P- 


■» 


o 


CC 


-c 


ro 


in 


^r 


ro 


—< 


O 


—1 


u 


< 








—> 




r-> 




p-4 


p~< 


















UJ 


OC 


X 




































> 


13 



IS) • 

m O 
4 Z 



•~ cm ro -4- in 



•— cm ro vl- m 



h rj c<- ^ ir, 



4 



o o 

Uj Z 

Cf. 4 

u- oc 



103 



r- ** od c\j r- 

(MMO hP 



r- r~ m <\i oo 





-i O 


UJ 


«M CM f» IT CI 


m 1-4 o o o 




3 — 


to 


CI —• O O O 


o o o o o 




< 4- 


< 


o o o o o 


o o o o o 




a « 


u 


• • • • 4 


• • • t • 




a 

>- 

1 o 




o o o o o 


o o o o o 












z 








to 


at ■— 


fl 


Old ^ OO 


cm r- r* o >»■ 


UJ 


< a 




MAIfl OrJ 


fiO^Md 


fr- 


uj x 


UJ 


tn e> «n * m 


■* -< o o o 


r- 


z < 


tO 


(M O O o o 


o © o o © 


at 


— o 


< 


o o o o o 


o o o o o 


UJ 


-J 


U 


• • 4 • • 


• • • • • 



a 

a 



© o o o o 



o o o o o 



m «#• •# o od 

4imhmO 

o o o o o 

o o o o o 

o o o o o 

4 • t • t 

o o o o o 



r~ m * o od 

O O O O O 

O O O O O 

o o o o o 

4 4 • • • 

o o o o o 



4 ~ 


in o vO -*• m 


O to 


M«*l(\0 


uj o. 


0- o co — r- 


a. o 


CM (B rn 0> •* 


U. mm 


OOhhn 



o o o o o 



in O CO <t> %f 

o -< r- m m 

r- r» cr o ■— 

«r <c * t> m 

<\j so — i in o 

4 4 4 4 4 

© © — i —> rv 



.* CM Ct a cr 

m <o ci o •-* 

-- vt CO N (> 

OKMI 4* 

m o cr *o -*■ 

4(444 

— j- ,o a <m 





c 




a) 




c 




o 




a. 




E 




O 




O 




oo 




1 




•> UO 




o o 




<3- • 




en 




i— ii 




«< (/> 




cu ca 




.&£ 




ra 




3 • 




O" E 




-C o 




+-> '1- 


ro 


S- -M 


• 


03 3 


00 


UJ i — 




O 


a> 


O CO 


r— 


S- 


.a 


+J c 


ca 


c o 


(— 


0) T- 




C_> +-> 




co 




■— s- 




LU CD 




a> 




O 4-> 




4-> £Z 




t— ( 




_l 




r— +-> 




O 




E <u 




CU s- 




+-> ■!- 




to Q 




>> 




00 



o 

or. 

O 



CD 
CO 

o 

a. 
to 

cu 

or 





a c 


























o 






o 


z 


— • «\j m 


-* 


in 


4*1 


<M 


ro 


•* 


in 


•-• CM 


ro 


■* 


m 


< 






z 


< 


























oc 

o 

UJ 

I 

4- 






v. 


OK 


in in in 


-* 


mm 


m4 


ro 


>t 


O 


O 


4- r- 


in 


co 


a 








CM 


a 


co ro co 


o 


•4 


0^ 


-J- 


nj 


o 


O 


O K 


CM 


m0 


•o 


UJ 










o> m o- 


o 


«NI 


00 O 


•o 


-1- 


•4- 


O cr 


mm 


wm 


~m 


Psl 






UJ 


_i 


o> o a 


o 


O 


ff 


O 


O- 


o 


O 


o cr 


O O 


O 


mm 






to 


< 


a- o o> 


o 


O 


cr 


© 


cr 


o 


O 


o cr 


© 


O 


O 


or 






< 


3 


4 4 4 


4 


4 


4 


• 


4 


4 


4 


4 4 


4 


• 


4 


< 






l_> 4- 


o — o 


m* 


— 1 


o 


mm 


o 


~m 


-* 


4- O 


*-* 


■H 


•—! 


UJ 








o 


























z 








« 


























_l 




u. 




o 


























o 




o 


■*» 


< 


ao t-i ao 


ro 


in 


p-4 


rj 


>t 


<o 


<o 


o c. 


~o 


o 


-4 


4- 




to 


f— 1 


or 


CD 0* CO 


O 


m 


4- 


ro 


ro 


CM 


00 


O h- 


*-4 


mO 


o 






z z 




Q 


0* OD O* 


O 


^t 


■o 


o> 


in 


CM 


CM 


o cr 


-1 


mm 


mm 


o 




o o 


UJ 




9- O 0> 


O 


o 


0> 


o- 


cr 


O 


O 


O cr 


o 


o 


O 


UJ 




to — 


to 


_l 


»o» 


O 


o 


a 


a 


Cr 


© 


o 


o cr 


o 


o o 


KTl 




mm m 


< 


< 


4 4 4 


• 


4 


4 


4 


• 


4 


4 


4 4 


4 


4 


4 


3 




or 3 


o 


3 


o .-. o 


-m 


— < 


c o 


O 


mm 


m4 


-i o 


mi 


m* 


—4 






< _j 




t- 


























on 




0. o 




«J 


























p- 




Z to 




< 






























o 






























4M 




u 


v» 




























Z 






o 




CO (M — 


<r 


o 


ro 


<t 


ro 


r-* 


00 


■O 4- 


(NJ 


■G 


mm 


UJ 






< 


O 


0> in o 


(Si 


ac 


fVJ 


in 


nj 


in 


oc. 


•o cr 


in 


CM 


ri 


_J 






or 


<r 


a CO o 


m 


00 


m 


^-i 


►» 


ro 


r- 


f» r- 


>* 


-* 


•* 


00 


UJ 




O 


at 


a r- o 


a 


00 


as 


O- 


cr 


CO 


00 


cr cr 


cr 


cr 


cr 


O 


o 






O 


o> o> o 


cr 


a 


o> 


a 


cr 


cr 


a 


cr cr 


CT 


<J 


a 


or 


at 




-i 




4 4 4 


• 


4 


4 


• 


• 


4 


4 


4 4 


« 


4 


4 


a 


o 




< 


a 


o o -> 


o 


o 


o o 


o 


o 


O 


o o 


O 


o 


o 




u. 




3 


z 


























o 






4- 




























< 


o 




O 




























at 


< 




< 




























c 

-J 

<r 


at 

o 

LU 








■C m r»> 


^3 


00 


<o 


•o 


r- 


in 


in 


r- er 


<f 


in 


ro 


3 


X 






(\j 


imOco 


<M 


m 


a 


r- 


cr 


<C 


* 


mt ro cr 


--* 


mm 


4- 


4- 


z 






m <© o> 


►- 


r- 


r- 


m 


<y 


CO 


00 


r- «<■ 


o 


CM 


■4 


<_> 




UJ 




UJ 


r-no 


o> 


m 


o 


oj 


<M 


oc 


o> 


00 o 


■4- 


CO 


•c 


< 


lii 


UJ 


O 


</> 


M 0*- nj 


CO 


f> 


h- 


mm 


■C 


CM 


o 


m cm 


■£l 


cr 


CI 




CM 


Z 


< 


< 


4 4 4 


4 


4 


4 


• 


■ 


• 


4 


4 4 


• 


4 


4 


Z 


mm 


4- 


a 


u 


00 CO 00 


f- 


<£ 


CM 


CO 


in 


* 


CM 


ro cm 


mm 


o o 


■— « 


at 


UJ 


O 










f-t 




















< 


(C 






























O 


UJ 


•« 


or 




























UJ 


z 


4- to 


<■ 




f- -O 00 


o 


© 


f- 


<N O 


CO 


00 


cm cr 


O 


CO 


o 


4- 


H 


Z UJ 


UJ 


*M 


m f* o 


(M 


O 


tf> 


r- 


O- 


m* 


(NJ 


O CM 


CO 


o 


r~ t 


3 


-J 


uj z 


z 




m r^ o 


r- 


a> 


(T 


>o 


»t 


m* 


•O 


r~ ^ 


O 


CM 


«r 


a. 




Z O 


M 


UJ 


f- •* -4 


a- 


* 


r- 


t-t 


CM 


00 


cr 


00 o 


•* 


ro 


•o 


z 


o 


UJ Z 


-1 


to 


C>J 0* »vj 


09 


w 


<o 


^^ 


<o 


(M O 


ro cm 


<0 


a 


Ct 


o 


K 


«-> mm 




< 


4 4 4 


4 


4 


4 


4 


• 


4 


4 


4 4 


• 


• 


4 


u 




< — 




o 


OD 00 CO 


f- 


<o 


<M 


00 


m 


-I- 


CM 


CI CM 4-1 


o o 


4M 


O 


-J 












4>4 




















UJ 


a. o 






























to 


t/> 


to z 






























to 


3 


— 3 






fO <** *o 


m 


CM 


<0 


m 


Nt 


•*■ 


cr 


CM O 


O cr 


CM 


< 




u u 


-J 




in in o 


cr 


-* 


00 


<NJ 


IM 


m 


<M 


© a> 


cr 


m 


m 


z 


to 


a. 


< 


o 


-t) 00 ~> 


.c 


P>J 


pH 


nj 


*m 


•-" 


o 


t^ nT 


oo 


O Cl 




mm 


UJ o 


3 


4 


r» oo ^ 


0> 


<M 


CM 


CM 


m 


r- 


or 


00 o 


ro 


CI 


o 


I 




> 


►- 


at 


»VJ 00 <\J 


CO 


n 


f^ 


—* 


* CM O 


CI CM 


<c 


cr 


f\ 


u 


>• 


— u 


U 


u 


• t 4 


4 


4 


4 


4 


4 


4 


4 


4 4 


4 


4 


4 


«t 


4— 


*~ z 


< 




00 CD 00 


p" 


•o 


Psl 


CO 


in 


<• 


CM 


m cm t-i 


o 


o 


UJ 


— 


< < 












m* 




















v-> 


-j 






























U. 


O 


UJ to 






























o 


-J 


ac oo 






oo rg 4~ 


0» 


in 


<e 


<S1 


r- 


r- 


O 


•O 00 


CM 


>o 


o 




UJ 


< 






o<oo> 


»\) r- 


in 


m 


cr 


»— * 


cr 


a> ro 


cr 


a 


-0 


>- 


> 


z z 




e 


>o m o 


«» 


r»> 


r\j 


m~ 


^0 


ro 


IT. 


^ a 


r- 


m 


in 


4- 




3 


o 


< 


f"- 00 mm 


n 


C» 


■-4 


0> 


<o 


<J- 


mm 


cr o .* ro 


■c 


M 


o 


Z 


z 


a 


MOW 


cr 


»n 


o 


mm 


>0 P" 


m4 


CI CM 


•o 


cr 


CI 


u 


z 


mm 




o 


4 4 4 


4 


4 


4 


4 


4 


4 


4 


4 4 


4 


4 


4 


o 


3 


X 






00 0^ 00 


P» 


<o 


(M 


CO 


m 


^ 


CM 


CI CM 


— < 


o o 


_J 


o 


< 












•-* 


















UJ 


at 


X 


1/1 


• 

o 


























> 
1 

mm 


O 
1 

CM 




< 


z 


HNn 


~r 


in 


•-4 


(N 


ro 


<f 


m 


mm rv. 


ro 


>r 


m 


UJ 


UJ 




z 




























l/> 

< 


to 

< 



4 UJ 



at < 

u- or 



104 



CO 

CD 

.a 

(0 



e 




CD 




E 




o 




Q. 




E 




O 




o 




OO 




1 




0, 


, 


o o 


<3- 


• 


CTi 




"-" 


II 


A 


to 


cd 


CO. 


£6 




re 




3 


• 


O" 


e 


-E 


o 


-t-> 


•1— 


S- 


4-> 


rO 


3 


LU 


r— 




o 


o 


00 


s- 




+-> 


e 


c 


o 


<1) 


•r— 


o 


+■> 




fO 


1 — 


S- 


LU 


o> 




CD 


o 


+-> 


4-> 


E 




►— 1 


s: 




r— 


+-> 




U 


E 


CD 


CD 


S- 


+J 


•r™ 


to 


Q 


>> 




00 




4- 




O 




CD 




CO 




c 




o 




Q. 




to 




CD 




ct 







u 




eg 


g* «m r- * <• 


>«■ ♦ ^4 


P-i -c 


p4 


no 


00 


O 


•c 








•— t 






O'^hNO' 


f O'MMff' 


pr ( 


<«■ 


CM 


IN 


mm 








-J o 


UJ 


IT* *ON 


h- eg _■ 


— o 


«— . 


o o © o 








3 


■M 


OO 


ONHH 


o 


O O O 


o o 


O 


o o o o 








< 


t- 


< 


o o o o o 


o o o o o 


O 


o o o o 








ac < 


u 


• • • • 


• 


• • • 


• • 


t 


• 


• 


t 


• 








O ar 




o o o o o 


o © o o 


o 


o 


o 


o 


o 








5 


o 

z 


























oo 


a 


■— 


1*4 


m f- pn eg •-< 


in pn p- 


43 4J- 


m 


43 


p> 


a 


m 






UJ 


< Q. 




OlflB^ 


m 


<r ^ m co * 


eg 


^t 


CM 


mm 


— * 






P4 


UJ 


X 


UJ 


O'IP't o 


CO 


— i + pj 


t— I ^4 


wM 


o 


o 


o o 






»- 


Z < 


oo 


43 pg _■ mm 


o 


-< o o o o 


o o 


o o 


o 






o- 


•— 


c 


< 


o o o o c 


o o o o o 


o o 


e 


o o 






UJ 


-J 




u 


• • • • 


• 


t • • 


• • 


t 


• 


• 


• 


• 






a. 
o 

a 








o o o o 


o 


o o o o o 


© 


o 


o 


© 


o 










t *■% 


lt\ ro ■* m 


in O co gj ■* 


4)- eg 


rr, 


cr 


C 






_) 






O 00 


p- en jf- m 


o 


O — h- 


m m 


m 


•c 


f. 


rr\ 


mm 






< 






UJ O. 


0' o or — < 


p- 


r* t- 0> 


o — 


•-» 


<t 


00 


p- 


I3> 






o 






0C (_> 


eg eo m <J> 


<« 


gj- <© •» 


a> m 


o 


IT 


ao 


•C 


43 






o 






U. — 


o o •— —< 


eg 


eg 43 -4 


m o 


m 


o 


CP 


-O 


41 






X 








• • • • 


# 


• • t 


# t 


t 


• 


• 


9 


• 


UJ 












o o o o o 


© o -* 


— i eg 


f-4 


>!• 


o 


CP 


eg 


l_> 




























mm 


ac 
o 

IL 










UJ • 






























a o 




















O 










o z 


mm eg fp >*■ 


in 


HNIH 


gf m 


t— 1 


rg 


p-, 


-t 


m 


< 










X 




















ec 

o 

UJ 










o 




















X 










< 




















»- 










«v ac 


in in r- •-< 


.-i 


p- 0" ei 


«» r- 


43 


^4 


in 


p- 


p- 












(M o 


tn O m «-• 


o 


f-4 *-4 P" 


o r- 


00 


_t 


rtNO 


UJ 












0* p- 0" -o 


0> 


eg x p- 


Pf) 43 


P- 


ITi 


43 


co 


o 


pj 










UJ -1 


cr —• cr p- 


rm 


<T 0» 43 


m <o 


CP 


0" 


0- 


o- 


o 


•— * 










oo < 


c o 0" cr 


o 


O* O 1 ff 


o o 


CP 


o- 


o- 


o- 


o 


oc 










< 3 


• • • • 


• 


t • • 


• • 


• 


• 


• 


• 


• 


< 










•_> I- 


o •-> o o 


-H 


o o o 


*4 — - 


o 


o 


o 


o 


•— 1 


UI 










CJ 




















z 










< 




















-1 




u. 






o 




















o 




o 






«^ « 


niniTN 


gs 


eg o p- 


CO o 


eg 


o 


fsl 


p- 


rr. 


K- 




V) 






— i a 


IT> •-< ITN IO 


^4 


O 43 oo 


O «!■ 


O 


O 


o 


00 






z z 






Q 


amco 


ao 


43 p- P- 


eg P- 


O f- 


00 


© 


mm 


o 




a o 






UJ 


ff^>N 


^H 


P- P- m* 


-4 >* 


O 


CP 


CP 


o 


O 


UJ 




v> — 






00 _J 


o o o a 


o 


CP cr o~ 


O O 


O 


CP 


o- 


o 


O 


00 




•-p- 






« < 


• • • • 


• 


t • • 


• • 


• 


• 


• 


» 


• 


D 




a. 3 






o 3 


o ~> o o 


I-l 


o o o 


f-4 —t 


■-■ 


o 


o 


t— 1 


•-i 






< -J 






1- 




















oo 




a. o 






u 




















*-« 




x uo 






< 
























o 


























-^ 




o 






«v 




















X 










o 


o O" r» eg 


<r 


CC H s 


eg O 


<y 


o 


-1- 


~0 


m 


UJ 










•* o 


o> it cr rr\ 


o 


w m r- 


eg co 


p- 


>0 


PsJ 


on 


eg 


-J 










a < 


<f rr\ o- in 


eg 


IAH4) 


•O fr\ 


o> 


r- 


oc 


r- 


p- 


OD 


UJ 








a ac 


^ (D C^^ 


eg 


P- 43 CO 


t- O 


41 


m 


in 


m 


m 


□ 


o 








a 


C 4 CO o* cc 


0* 


CP (^ 0D 


CD <P 


0> 


cr 


cr 


CP 


o> 


ec 


ac 








-j 


• • t • 


• 


• • • 


• • 


• 


• 


• 


« 


• 


a. 


o 








< o 


o o o o 


o 


o o o o o 


o 


o 


o 


o 


o 




u. 








3 Z 




















o 










p- 




















< 


o 








O 




















ac 


< 








« 




















a 

-> 
< 


a 
a 

UJ 










fi o ■*■ fl 


<c 


CP P- o 


m co 


p- 


p- 


~r 


CO 


m 


3 


X 








eg 


IMAC'O' 


n 


O rri 43 


0" 43 


43 


>t 


>r 


o 


•-• 


l~ 


»- 


z 








o* tr eg >r 


m 


cd eg m 


O r» 


0> 


(NJ 


CD 


-* 


» 


U 




UJ 






UJ 


rtHflft 


p- 


irpjg; 


oo cp 


p*l 


o 


or 


cc 


in 


< 


UJ 


UJ 






O oo 


m o <*^ eg 


gj 


gj- CP eg 


co m 


43 


o 


CP 


o 


43 




pg 


X 






« < 


• • • • 


• 


t • • 


• • 


• 


• 


• 


• 


• 


z 


— 


p- 






ac u 


00 O CO 0* 


gj 


^ffMflW 


m 


^^■ 


eg 


I-l 


o 


•— 


ac 


UJ 






a 


p-4 




v* 
















< 


as 


























o 


UJ 


mm 






ac 




















UJ 


z 


P-00 






< 


IMClfilfl 


o> 


pn 43 -t 


43 f~ 


m 


sr 


»f 


43 


00 


K 


1-4 


zui 






UJ •- 


r- r«- r- o 


r- 


43 ■« •» 


■4 m 


co eg o 


<-> 


eg 


3 


-1 


UJ X 






z 


o» g3 eg eg 


a> 


eg p- pg 


eg eg 


p^ 


o 


41 


1- 


o 


0. 




X o 






— UJ 


o"i <r p-, co 


43 


eg «-< p- 


m ro 


in 


w-< 


a 


00 


43 


X 


o 


UJ Z 






-J l/> 


m o> e^ — < 


49 


eg r- co 


<o m 


<o o a 


<c 


43 


o 


»— 


O •- 






4 


• • # • 


• 


• • • 


• • 


# 


• 


• 


• 


• 


u 




«3 — 






u 


CO 0* CO 0* 


gj> 


<» Cf 43 


m pn 


in 


gj- eg 


1-1 


o 


•jr 


Q 


-J 












PC 
















UJ 


a a 


























O0 


oo 


00Z 


























(/) 


_i 


— 3 








co r- m a- 


o> 


eg eg r-i •>< o 


e- 


m 


00 


<■ 


00 


< 




o o 






-J 


■o u-v in <7- p- 


•-< m pn p» m 


r- 


f-i 


<r> 


CP 


o 


X 


oo 


ac 






< o 


^ r- <o « o 


eg O p- 


>*■ eg 


** eg 


CP 


gj 


cr- 




•-• 


UJ o 






3« 


g;*m« 


in 


p-g/ojBp 


m 


eg 


CP 


00 


m 


X 




> 






»- ac 


pn co pi> •♦ tr\ 


m a ■* m rr, 


« o cr 


43 


>o 


u 


> 


— a 






uu 


• • • • 


• 


t • t 


t • 


t 


• 


• 


• 


• 


<l 


•- 


H-Z 






« 


OB 0" CO C 


•c 


>»■ o> r- 


m m 


w\ 


•* 


eg 


«-< 


o 


UJ 


•— • 


< < 












p4 
















u 


-J 


























U. 


D 


UJ to 


























O 


-j 


ac </> 








gj iri eg eg -O 


0» P- "4 


tr\ P- 


•* m 


1*1 


43 


1*. 




UJ 


< 








p- a> co < eg 


0» p-i eg 


$?. 


m eg p- 


mm 


in 


>- 


> 


X X 






o 


m >»- -o co -*■ 


pg O eg 


o a 


© 


f-i 


00 


t- 




3 






§2 


■& •* m o 

P?> •-• P^l CD 


o 


* «* 4) p- pri 


m o 


rr, 


43 


CD 


mm 


o 


X 






v^ 


cp fo 4r 


f\ p- 


CP 


eg 


•■* 


P- 


43 


u 


z 


M 






a 


• • • t 


• 


• • < 


• • 


• 


• 


• 


• 


• 


o 


zs 


X 








«HCor> 


•» O 00 


g3 en 


m 


41 


m 


~m 


O 


-J 


o 


< 








••4 -* 




-* .-4 














UJ 


ac 


JL 


























> 


o 



oo • 

mo 



• UJ 



ac « 
u. ac 



t-< eg rr, ■+ in 



r-> eg rr. ■4- m 



H(MI<l4l« 



< 






105 





+-> 




c 




CU 




£ 




o 




Q. 




E 




O 




o 




00 




1 




•> lo 




o o 




•3- • 




CTl 




r— II 




« 




CU GO. 




_*. 




<T3 




3 • 




O" E 




-C O 




-M 't- 


LO 


S_ +-> 


• 


CO 3 


CO 


LU i — 




o 


CU 


O OO 


r— 


S_ 


-Q 


+J E 


<T3 


c o 


h- 


CU -r- 




CJ> +-> 




n 




r— S- 




UJ CT> 




CU 




o +-> 




+-> c 




t— 1 




s: 




r- +-> 




o 




E <U 




CU s- 




4-> -r- 




l/) Q 




>> 




00 





u 




CM 


<* «m p- <• <■ 


>♦ •* mm co <o 




M 






0* * •-" CM o» 


»ffh-Nff 




-I o 




UJ 


ir> ■* •* o p- 


NNHhO 




3 — 




oo 


^imhhO 


o o o o o 




4 P- 




4 


o o o o c 


o o o o o 




(X 4 




O 


• • t • • 


• • • 9 • 




>- 
X o 






o o o o o 


o o o o o 














z 










on 


at «" 




— i 


m o cp <o co 


cm cm •*• co cm 


UJ 


< a 






ir^Nnm 


<o od >c •-• a 


MM 


UJ X 




UJ 


N»H«4 


hN»4HO 


»- 


z 4 




</) 


m -> ~* o o 


o o o o o 


a. 


•- o 




< 


o o o o o 


o o o o o 


UJ 


-J 




o 


• • • • • 


• • • t • 


a. 








o o o o o 


o o o o © 


o 












a. 












a. 
















t 


MM 


ir\ p\ -C •* v\ 


in o ao o *i* 


-J 




o 


on 


p- co * m O 


O mm P- in m 


< 




UJ 


a 


f 0»nh 


f* p- cr o -m 


a 




a 


u 


(MOOCIO-* 


* <© * a ir 


o 




u. 


*m 


OOhhN 


N^Hiro 


X 








• t • • • 


• • • • • 



o o o © o 



O O H H W 



h eo a o 4 

co «*■ im im t— 

— o o o o 

o o o o o 

o o o o o 

• t • • • 

o o o o o 



■C in — ■ ITi CM 

or co cm —t —> 

o o o o o 

o o o o o 

o o o o o 

• • • • • 

o o o o o 



«$ cm co cr CP 
in.ccom.Mi 

,-i ,»■ oo p- cr 

O in CD mD -C 

m O CT -C «T 

• • • • • 

-i -jj- -c cr ini 



o 
a: 
O 

u. 



cu 

£Z 

o 
a. 
</> 

CU 





o o 
























o 






o z 


•-* IM 


CO 


^ 


m 


f-< CM CO 


4 


in 


MM 


<\J 


r 


<t in 


< 






X 
























CC 

Q 

UJ 






(9 
























X 






< 
























t- 






>v QC 


o *- 


en 


-c 


*-4 


•om p- 


•C 


CM 


in 


in 


in 


«» O 








CM O 


sO cr 


r- 


cc 


P- 


O 00 00 


■c 


<»■ 


CO 


ao 


in 


CM CO 


Ul 








a o 


(7- 


cr 


<o 


oo in o 


oo 


in 


00 


p- 


00 


cr cr 


M 






UJ _J 


O |«4 


a 


a 


^M 


oo a o> 


cr 


o 


cr 


o- 


cr 


cr cr 


MM 






in < 


a o 


o 


0" 


o 


o^ cr cr 


cr 


o 


cr 


cr 


cr 


cr cr 


or 






< 3 


• • 


9 


• 


• 


9 9 9 


9 


9 


9 


9 


9 


9 9 


< 






o *- 


o --> 


o 


o 


•M 


o o o o 


MM 


o 


o 


o 


o o 


UI 






u 
























z 






< 
























-1 




u. 


o 
























o 




o 


«v < 


m 0> 


co 


in 


>»• 


CM 0* 00 


-£ 


CO 


p- 


§ 


CM 


cm m 


M- 




I/I 


— i Of. 


h- tr> 


p- 


oo 


CO 


co jj- co 


-O 


o 


m 


ao 


•» •» 






z z 


o 


o> r~ 


cr 


<? 


o 


0^ •£ H 


cr 


« 


or 


a 


c 


MM wM 


o 




o o 


UJ 


C* !-• 


o- 


V 


CM 


oc cr a 


cr 


o 


cr 


a 


o 


o o 


UJ 




on MM 


to _J 


a o o> 


1- 


o 


cr cr cr 


cr 


o 


cr 


a 


o 


o o 


00 




— r- 


«* «I 


• • 


• 


• 


• 


9 9 9 


9 


9 


9 


9 


9 


9 9 


3 




oe 3 


O D 


o — 


o o 


f-H 


o o o 


o 


f-9 


o 


o 


—* 


w-4 w* 






4 _j 


K 
























oo 




a. o 


o 
























M- 




x «/> 


< 




























o 


























M 




o 


^ 
























X 






o 


O IT 


o 


o 


in 


CM CO CO 


*— 1 


p- 


o 


CO 


ao 


co O 


UJ 






< o 


o r^ 


o 


IT. 


CO 


CO 9-1 9-4 


■* 


* 


o 


-O 


a- 


<o P- 


_l 






oc < 


o r^ 


O IT 


<o 


OO « 


■0 


ao 


p- 


r- 


CM 


CM CM 


CD 


UI 




o or 


o tri 


o 


cr 


<o 


oo oo cr 


p> 


p» 


V 


cr 


Cr 


cr a 


O 


o 




a 


O tf 


o 


<y 


O 


cr <t* cr 


cr 


cr 


0> 


cr 


O 


cr cr 


or 


cc 




-J 


• • 


t 


• 


• 


9 9 9 


9 


9 


9 


9 


9 


9 9 


a. 


o 




< c 


—l o 


f-« 


o 


o 


o o o 


o 


o 


o 


o 


© 


o o 




u. 




3 Z 
























o 






»- 
























4 


l£ 




u 
























or 


4 




< 
























o 

_j 

4 


OC 

a 

UJ 






«*■ o 


»v 


in 


«t 


CM — 1 CO 


c 


MM 


o 


MM 


cr 


•C P- 


Z) 


X 




CNJ 


oo m 


r- 


ir, 


00 


CM P- IT 


o 


& 


* 


~t 


cr 


co -G 


1- 


r- 


z 




fn >t 


00 


p> 


—) 


P- O CO 


in 


MM 


o> 


O- 


CO 


00 CM 


o 




UJ 


UI 


r^ <r 


o 


r> 


CO 


O «3 cr 


CO 


00 


p- 


B> 


ro 


CM W5 


4 


Ul 


UJ 


O </l 


CM h- 


<NJ 


OC 


CM 


m O in 


<M 


o 


co 


W-* 


>o 


a CO 




MJ 


X 


< < 


• • 


• 


• 


• 


9 9 9 


9 


9 


9 


9 


9 


t • 


Z 


MM 


P- 


C£ O 


00 00 


00 


h- 


-0 


cm oo m 


* 


CM 


CO 


CM 


W-* 


o o 


MM 


CC 


IU 


Q 










9H 
















4 


CO 


























a 


Ui 


MM 


St 
























UJ 


z 


P- 00 


4 


1*1 CM 


r- 


>♦■ 


a 


IfllMM 


P> 


P- 


•fl 


P- 


o 


cr m 


r- 


MM 


Z UJ 


UI tx 


4- -< 


•-i 


>» 


CM 


i->04 


CM 


W 


IT. 


o 


p- 


CO .* 


3 


-1 


uj x 


z 


•» M. 


0- 


r~ 


< 


CO IT. <0 


or cm 


CO 


CM 


r- 


O CO 


a. 




X «_> 


— uj 


t^ ir 


o 


o 


o 


cm * cr 


CO 


ao 


ao © 


co 


CO tV 


X 


o 


UJ z 


-J oo 


CM CO 


(M 


oo 


CO 


m o m cm O 


CO 


CM 


m3 


CP CO 


o 


r- 


O "- 


< 


• • 


• 


9 


9 


• 9 9 


9 


9 


9 


9 


9 


9 9 


u 




< «-■ 


u 


00 00 


eo 


r- 


<o 


CM CD in 


■* 


CM 


CO 


CM 


^ 


o o 


«M» 


O 


_J 












9-9 
















UJ 


0- o 


























oo 


oo 


OO z 


























00 


-> 


•- 3 




-*■ ir> 


-» 


CM 


r-4 


CD O *C O 


OO 


o 


m 


in 


•o CO 


4 




O U 


_l 


•O CD <3" 


<o 


-t) 


CO CM O 


r- 


CO 


o 


^•t 


CO 


o a 


X 


</> 


DC 


< C9 


« o» 


o 


CO 


ao 


co <r uo 


o 


o 


m 


<r 


*J 


CP CM 




MM 


ui o 


3 « 


P- IT 


M* 


tr 


P- 


in or * 


* p- 


CO 


O CO CM •*) 


X 




> 


»- oc 


CM -O 


CM 


0D 


9-* 


o o <c 


CM 


w 


CO 


CM 


W5 CP CO 


o 


>- 


— u 


1_> LJ 


• • 


• 


9 


9 


9 9 9 


9 


t 


t 


9 


• 


9 9 


•» 


f— 


t- z 


•X 


ao co 


co r~ 


>0 


cm oo m 


•t 


CM 


CO 


CM 


w~* 


o o 


UJ 


MM 


4 4 












9-1 
















u 


_J 


























u. 


o 


UI O0 


























O 


-J 


a on 




ao cm r- 


t> 


m 


O CM P- 


P- 


CO 


■a 


oo cm no c 




UI 


4 




•o ~o 


c* 


CM p- 


m in or 


«-* 


or 


cr 


CO CP 


or O 


>- 


> 


X X 


o 


■e m o 


»»• en 


CM 9-1 <o 


CO 


in 


,«• cr 


P- 


m m 


r- 




3 


gs 


t- 00 


•-i 


co cr 


_< cr o s 


w^ 


cr 


o 


>r 


CO «c 


MM 


a 


X 


CM O 


CM 


<p 


CO 


or r- o 


CO 


9*4 


CO 


CM 


Mj 


CP CO 


u 


z 


MM 


a 


f • 


• 


t 


9 


• • • 


9 


9 


• 


9 


9 


9 9 


o 


3 


X 




oo e 


0D 


r- 


<© 


cm oo m 


^- CM 


CO 


CM 


MM 


o o 


_l 


o 


< 












9-1 














UI 


CC 


X 


vo a 
























> 
I 


U 
1 

CM 




< z 


HNW 


9»Nldg> 


in 


MM 


CM CO 


UJ 


UJ 




X 
























00 

4 
U 


oo 

4 
l_> 



• UI 

ao 

UJ z 
cc 4 
u. CC 



CO 



106 



CM 



LU 



_l O 
3 ~ 

< K < 
BC ■< O 

O cc 

>■ 

r o 

z 

fX «- .-I 

< a. 



z < 





+J 




c 




a> 




c 




o 




Q. 




E 




O 




o 




oo 




Z 




m 




O i— 




«=* o 




cr> • 




1— ■ 




II 




•> , 




a> aa 




.^ 




ro 




3 • 




O" c 




-E O 




+J -r- 


l£> 


S- +-> 


* 


fO 3 


CO 


LU i — 




o 


CD 


O C/J 


^— 


s- 


XI 


+-> c 


n3 


c o 


1— 


aj •■- 




o +-> 




fO 




i— s- 




LU CTl 




<U 




O +-> 




+J £Z 




i — i 




_J 




CM +J 




O 




E cu 




a> s- 




+j -r- 




to Q 




>> 




oo 



l/> 

< 



o> I/) 

uj a 
a: o 



m •- od m r~ 

00 W 4 -O ff 

CO f- O O O 

o o o o o 

• • • • • 

o o o o o 



r~ d © od *h 

CO ^ CO m O 

m -- o o o 
o o o o o 

• • • • • 

o o o o o 



o> •>» o> m m 

•— -C .-« O r- 

OOhNN 
• t • • t 

o e o o o 



P- *C m o -* 

o •* cc o m 

co ••• o o o 

o o o o o 

o o o o o 

• • • • • 

o o o o o 



r- #-< -* p- -t 

IMMHOO 

o o o o o 

o o o o o 

• • t • • 

O o o o o 



m cm •* 0" cm 

o o «o o r~ 

p- »*■ m o o- 

■4 p- r- en —< 

cm *o —> •© o> 

• • • • • 

o o •-« •-* •"*■ 



«f> <• -4 O «D 

■e i\i w — o 

o o o o o 

O O O O O 

o o o o o 

• • • • t 

o o o o o 



(> fO ff- fn h 

oc en —. _ i — 

O O o o o 

o o o o o 

O O o o o 

♦ • ♦ • • 

O o o o o 



•4- o a> en o 

m .© -4 en o 

.-< * m cm oo 

in o •— < o~ *c 

■ • • • • 

.- ^ r- o .-* 



o 
a: 

o 



to 
o 

Q. 
10 
CD 

a: 





o o 


























o 






o z 


•j(vin 


•* 


in 


■—i 


cm en 


>» 


u> 


f* 


rj 


CO 


-4 


in 


< 






z 


























a 

UJ 






o 


























I 






< 


























*- 






>s QC 


o r- <\i 


a* 


■4" 


^- CM 00 


o 


nO 


or- 


f~ 


ao 


O- 








<\J Q 


it* oo oo 


-» 


r»- 


in 


t-4 00 


r- 


* 


«* 


in 


O f- 


<J3 


UJ 








(VO- 


»SI 


o 


00 


cr co 


m 


CM 


CM 


w~* 


CM 


<M 


CM 


Psl 






UJ _l 


h- o< h- 


o- 


o 


0> 


0- o 


<M 


CM 


O 


O 


o o 


O 


1-4 






to < 


0*0*0* 


a 


o 


a 


o> c 


o 


O 


o 


o 


o 


o 


O 


BC 






< Z) 


• • • 


• 


t 


• 


t • 


t 


• 


• 


• 


• 


• 


t 


< 






O 1- 


o o o o 


—t 


o 


o -< 


»-i 


f-4 


p>4 


—* 


•-> 


•-I 


•— • 


UJ 






u 


























Z 






< 


























-I 




u. 


o 


























o 




o 


>» < 


•* o <t> 


t 


o 


>o 


CO ro 


in 


in 


O 00 


in 


CM 


►- 




«/> 


i-i a. 


•t o o 


CM 


r^ 


O CO 


O- 


CO 


a 


r~4 


yD 


m 


CM 






z z 


a 


l*> «M vt 


ro 


,_* 


«* 


*»■ r~ 


•4- co 


o o o 


*-t 


«—l 


o 




o o 


UJ 


(k. O h. 


a- 


o 


o> 


<y 0* 


w* 


.-< 


o o 


o 


o 


o 


Ul 




to •— 


to _) 


o> o* o> 


o- 


o 


o> 


o- a* 


o 


O 


o 


o 


o o 


o 


to 




f. 1- 


< < 


• • • 


• 


t 


• 


• # 


• 


• 


• 


• 


• 


• 


• 


3 




0C 3 


O 3 


o o o 


o 


^4 


o o c 


•-H 


*-• 


p>4 


•—t 


••4 


*-i 


*-* 






< -I 


»- 


























to 




a. o 


O 


























(-4 




z •» 


< 






























o 




























«^ 




u 


^. 


























Z 






o 


w in in 


(7* 


•* 


r- 


ao a 


r- 


v-l 


CO 


m 


O 


IM 


o 


UJ 






< o 


in »-« r- 


O* 


00 


c 


vO CO 


•4 


CO 


in 


-o 


*~* 


ro 


CO 


-J 






ac «« 


in to <• 


IT* 


(M 


rn 


.-• f»- 


<\j 


00 


CO 


-* 


<t 


CO 


en 


00 


Ul 




Q a: 


O tr\ oo 


-*■ 


CNJ 


O* 


o> o 


in 


m 


o 


o- 


0> 


a 


fj» 


o 


u 




a 


O s 00 


o- 


0* 


0* 


o- o> 


0- 


O- 


o> 


a 


a 


a 


a 


ct 


ex 




-J 


• • • 


• 


• 


• 


• • 


t 


# 


t 


• 


t 


t 


• 


a. 


a 




< a 


o o o 


o 


o 


o o 


O 


o 


o 


o 


o 


o 


o 




UL 




3 z 


























o 






k 


























< 


o 




o 


























ct 


< 




< 


























a 


cc 

a 

UJ 






<o <# r- 


-t 


(f 


in 


r«- cm 


-o 


CO 


PM 


CO 


CO 


CO 


<M 


3 


z 




«NJ 


•C •— rsj 


p-i 


o 


«0 


cr <o 


«t 


•-< 


r-- 


CO 


r~ 


,_< 


en 


K- 


t- 


z 




s o* <o 


0D 


CM 


>*■ 


no ao 


>»■ 


CM 


m 


ao 


o^ 


CM 


m 


O 




UJ 


UJ 


— u-i ^ 


-t 


r- 


«-4 


•- «* 


o 


c*> 


f- 


-t 


en 


•♦ r- 


< 


UJ 


UJ 


13 «/> 


t> «M •* 


ao 


•* 


<£ 


•4- r~ 


CT* 


r* 


*t 


o> 


IM 


*H 


•4 




CM 


X 


< < 


• • • 


• 


t 


• 


• • 


• 


• 


• 


• 


• 


• 


• 


z 


M 


K 


CL l_> 


OD O O 


ao 


•c 


rn o r- 


in 


CO 


en 


CM 


CM 


fH 


O 


"— • 


ex 


LU 


o 


-* »-l 






f-i 


w~t 


















< 


CD 




























o 


UJ 


«« 


(X 


























UJ 


z 


K »0 


< 


r»- «o m 


in 


•c 


r- 


-t cr 


■* CM 


CO 


a 


O 


>o 


CO 


»- 


•— 


z tu 


UJ — 


<M >» U« 


*> 


o 


«j f>- r*- 


m 


■4- 


in 


r- 


<0 


m 


«J 


3 


— 1 


uj z 


z 


00 — O 


>0 


in 


n 


CO CO 


CM 


CM 


O 


-* 


~Q O 


«4 


a 




£* 


♦— UJ 


*vj h- r- 


IT, 


h- 


<o 


r- <o 


>*■ 


O 


f- 


•* 


en 4- p- 


z 


a 


-J to 


<r »\j ■* 


OD 


<» 


in 


CO -o 


OD 


CO 


** 


or 


CM 


-^ 


«»• 


o 


»- 


o — 


< 


• • • 


• 


t 


• 


• • 


• 


• 


• 


• 


• 


• 


• 


u 




< «- 


o 


oo o O 


CO 


<o 


m 


o r- 


ir 


CO 


en 


(\j 


CM 


4—1 


O 


m* 


o 


-J 




»-« «-H 






M 


p4 


















UJ 


a o 




























to 


{/) 


to z 




























1/1 


-J 


-. 3 




U^ * O «NJ 


r- 


•-I m 


cr 


CM 


o 


in 


a- 


^H 


m 


< 




O O 


_l 


at) <A (M 


•-• 


CM 


m 


•-< **• 


-*■ 


o> 


>» 


CM 


o 


o 


O 


X 


lO 


uj C 


< o 


hwc 


u 


h- 


•* 


-c o 


■V 


CD 


p" 


T 


in 


o* 


•4- 




»— 


3 « 


r- u^ ■* 


•-I 


-o 


CO 


CM 00 


in 


m 


<o 


•* 


m 


ro 


P" 


I 




> 


t- ac 


#-< (<i r- 


c 


* 


<o 


«*• -o r- 


CM 


•* 


0> CM 


«— i 


•4 


o 


> 


— u 


i-t u 


t • » 


• 


• 


• 


• t 


• 


t 


t 


f 


• 


• 


• 


1« 


1^ 


p- z 


« 


a- o o co 


<o 


m 


o r«» 


in 


CO 


CO CM CM 


*— i 


o 


UJ 


l-N 


< < 




— < — i 






■-< 


w* 


















O 


-j 




























u. 


o 


UJ V) 




























o 


-I 


oc i/o 




O CM »0 !>• 


w* 


CO 


a- ,* 


CM CM 


CO 


-O 


* P- 


m 




UJ 


< 




IflCIMOO 


r»- 


m co 


l» 


a 


o* 


!•* 


eo O 


CM 


> 


> 


z z 


o 


cr> «r o» 


* 


ao 


«7> 


co a* 


ro 


00 


o- 


o 


CO 


-o 


p- 


K 




3 


o «t 


o* o »♦ CM o 


CM 


.-! CO 


-r 


tr 


00 


vO 


>!■ 


-t 


r~ 


M 


c 


z 


Z a 


•* o •* «r 


O 


f«- 


m o- 


o 


CO 


»t 


o 


CM 


•-I 


«#• 


u 


z 


»*• 


a 


• • t 


» 


• 


• 


• • 


• 


# 


• 


• 


t 


• 


• 


a 


3 


X 




Vhnc* 


f- 


CO 


o r- 


>0 CO 


tr 


<vj 


CM 


-* 


o 


_i 


Ul 


< 




*< t-l 






«-l 


r-l 
















UJ 


ex 


X 


to • 


























> 
i 


o 
I 

CM 




< z 


•-• CM f0 «t 


m 


f-4 


CM CO 


*t u> 


rat 


<M 


CO «* 


m 


UJ 


UJ 




X 


























1/) 

< 


to 

< 



• UJ 

a o 



oc < 
U. (X 



107 



a> 

e 
o 
a. 
E 
O 

o 





u 






CM 


in »— eo m t*- 


r- -c 


m 


o 


r-* 


lf> 


■* 


JOB 






■— 








od cn ■* ■£> rr 


o •* 


00 


•£> 


lf> 


•0 


CM 


— — o 






-1 o 




LU 


O ri <C -4" C» 


co r* 


o 


© 


o 


o 


o 


o o o 






3 


r-i 




0/> 


CO »— o o o 


o o 


O 


o 


© 


c 


o 


o o o 






< 


K 




4 


o o o o o 


o o 


o o 


o 


o 


o 


o o o 






or 


4 




u 


• • • • • 


• • 


• 


• 


• 


• 


• 


• • • 






O or 






o o o o o 


o o 


o 


o 


o 


o 


o 


o o o 






>■ 




























I O 




























Z 
























OO 


oc 


.-* 




r-4 


o —> r* <r <♦ 


t-i ro 


CM 


cr 


o 


r* 


c 


r- cm O 




ID 


4 


a 






irt tr i*> o <o 


cr •* 


00 


it* 


(ft 


oc 


m 


r-l r-l ft 




— 


LU 


X 




UJ 


O r- .<• co cm 


co r«4 


o o 


o 


o 


O 


o o o 




r- 


Z 


4 




00 


cvj O O O O 


o o 


o o 


o 


o o 


o o o 




a. 


— 


a 




< 


o o o o o 


o c 


o o 


o 


o 


o 


o o c 




Hi 


-1 






u 


• t • • • 


• • 


• 


• 


• 


• 


• 


• • • 




a 










o o o o o 


o o 


o 


o 


o 


o 


o 


o o o 




c 




























a. 




























a. 


































• 


r» 


0> •*• <T CO IT 


If i CM 


•* 


cr 


CM 


«» 


« 


cr co o 




-i 






O oo 


r~ r»- c\j cy O 


o o 


-o 


o 


r- 


If 


>o 


>»• co O 




4 






UJ 


0. 


•-« wa •-■ o r- 


r- «i- 


If 


o 


cr 


r-l 


^ 


if cm od 




o 






ac 


i_> 


ro ao if r- -j 


* r~ 


h- 


ro 


r-l 


o 


o- 


J o <o 




a 






u. 


fcr» 


oohnn 


cm «o 


«-l 


•o 


cr 


If 


o 


-c* 




X 










• • • • • 


• • 


• 


t 


# 


t 


• 


• • • 


UJ 












o o o o o 


o o 


r-l 


r-4 


r« 


r-< 


«* r» 


o 


























r* 


or 

o 

LL 








LU 


• 


























a 


o 


















O 








o 


z 


r-i CM CO •* If 


—> CM 


ro 


~1 


If 


w— 


r\j 


CO -» Ifl 


< 








X 




















(X 

O 



OO 





O LD 




«* o 




en • 




r— 




ii 




aid 71 




^ 




co 




3 ■ 




cr c 




-c o 




-t-> t- 


I**. 


s_ +-> 


• 


ro 3 


CO 


LU ■ — 




o 


<u 


o oo 


i — 


s- 


.a 


+-> c 


ro 


c o 


I— 


CD t- 




C_> 4-> 




rO 




r— S- 




LU a> 




eg 




O +J 




+-> c 




1 — 1 




_l 




C\J +-> 




o 




E CD- 




CD s- 




-M '1- 




CO O 




>> 




oo 




4- 




o 




CO 




t/) 




c 




o 




Q. 




w 




O) 




Di 





o 
































X 






< 
































K 






V. oc 


r\J 


r- 


o 


(M 


00 


00 


O 


•* 


K 


CM 


■£ 


>1 


O f>- 


pn 








rg o 


09 


00 


LTl 


a- 


f^ 


c<> 


f- 


o o o 


f^ 


cr 


00 


m 


a 


UJ 








a 


a- 


»— 


cr 


o> 


r- 


<0 


r»- 


pH 


•O 


r«4 


r-l 


r-4 


•-i 


•—• 


KJ 






LU -J 


o> 


o- 


o 


<? 


0> 


o 


t> 


cr 


o o 


o o 


o o 


o 


H 






00 « 


0* 


a 


o 


a 


o> 


cr 


cr 


cr 


o 


O 


o o 


o 


o 


o 


ac 






< 3 


• 


• 


1 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


t 


<t 






(_> 1- 


o 


o 


^H 


o o 


o 


o 


o 


»~* 


•-i 


#-l 


r-i 


-H 


r-l 


r-l 


UJ 






O 
































z 






< 
































-J 




LL 


O 
































o 




o 


■V < 


00 


<\j 


o 


rsi 


If 


pH 


m r-- 


CM 


LT< 


cr 


o 


•»■ 


t- 




Irt 


f- OC 


0D 


a 


*0 


a 


a> 


Ifl 


00 


r— t 


(NJ 


CM 


o 


r-l 


o- 


** 


00 






z z 


Q 


<y 


a 


If 


a 


CVJ 


r~ 


vD 


r- 


r-l 


-O 


t— I 


r-l 


o 


o 


o 


o 




o o 


UJ 


o> 


o- 


o 


o 


o 


0> 


cr 


cr 


o 


o 


o o o o 


o 


LU 




l/> « 


00 _J 


o> 


o- 


o 


o- 


o 


o- 


cr 


(T 


o 


o 


o 


o 


o 


o 


o 


OO 




•-" K 


•< < 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


t 


z> 




ct O 


O 3 


o o 


•— • 


o 


f-4 


o o 


O 


r-l 


•M 


wt 


rH 


r-l 


r-l 


r-l 






< -J 


1— 
































oo 




a o 


U 
































■— 




X i/l 


< 




































a 


































r- 




u 


v. 
































X 






O 


iH 


oo 


rn 


•o 


rg 


4 


•* 


CM 


If 


r-t 


•—I 


OC 


r- 


*c 


CM 


LU 






< o 


o 


o 


w~* 


o 


OD 


~t 


cr 


m 


n 


rc 


r-i 


oc 


rr 


l» 


P- 


-J 






or. «t 


o 


V 


■£> 


o 


O 


4- 


«* 


■* 


o 


-C 


ifi 


>J 


J 


* 


CO 


ao 


LU 




O or. 


o 


o 


00 


o 


0> 


Cr- 


cr 


a 


cr 


r~ 


cr 


cr 


cr 


cr 


cr 


o 


l_> 




O 


o 


a 


a* 


o 


o 


C7- 


cr 


a 


cr 


cr 


cr 


cr 


cr 


a 


<r 


or. 


a 




-J 


t 


• 


• 


• 


t 


• 


• 


t 


t 


• 


• 


t 


t 


• 


t 


a. 


o 




< o 


vH 


o o 


»-< 


o 


o o 


o 


o 


o 


o 


a 


o 


o 


o 




LL 




3 Z 
































o 






»- 
































< 


o 




u 
































oc 


4 




« 
































a 

-j 

4 


CC 

Q 

LU 






r> 


.— * 


a~ 


rvj 


o 


o 


INI 


o 


IT. 


-t 


<c 


o 


cr 


o 


m 


3 


X 




fM 


o 


v0 


00 


-J 


<M 


o 


r-l 


o r»- 


ro 


a- 


r-< 


p\ 


if. 


O 


r- 


r- 


z 




a> 


m 


r-> 


■0 


(M 


cr 


f* 


4 


-0 


f- 


o 


a 


o 


0D 


«» 


O 




UJ 


UJ 


<0 


<»• 


o- 


r» 


o 


*»• 


<M 


•-* 


cr 


o 


r-r 


m 


if 


If 


if 


<I 


LU 


UJ 


O 00 


M 


(M 


o 


o- 


f—1 


w-t 


r- 


■G 


-* 


o 


r-i 


*o 


OP 


cc 


CO 




•VI 


X 


< < 


• 


• 


• 


• 


t 


• 


• 


• 


• 


• 


• 


• 


• 


« 


• 


z 


M 


H 


or. «_> 


00 00 


a- 


r-- 


<o 


CM 


ao 


^O 


«t CM 


m 


(V 


r-l 


o 


o 


r- 


OC 


Ul 


O 












p-i 






















4 


OD 


































o 


LU 


*^ 


oc 
































LU 


z 


1- vn 


4 


ifi ro 


IT 


■£) 


(M 


t— l 


CM 


CM 


-* 


oo 


00 


i— i 


cr 


r- 


Ifl 


K- 


— 


Z uj 


UJ •-" 


lf> o 


ci 


•* 


ID 


Ifl 


<M 


cr 


rn 


03 


-O O 


oo 


•C 


<o 


3 


_l 


UJ X 


z 


0» 


>*• 


<j- 


O 


^4 


o 


(M 


J 


r- 


r~ 


00 


r- 


•» 


t- 


o 


a. 




X o 


— UJ 


<0 


-r c\j r- 


(M 


Ifl 


<M 


r-" 


cr 


o 


O 


f\ 


If 


in 


m 


X 


o 


UJ z 


-J 00 


OJ 


cvj 


•-i 


CT 


*— > 


M 


r» 


-o 


>r 


o 


t— i 


o 


ao 


ao 


CO 


o 


»- 


<J •- 


< 


• 


t 


• 


• 


1 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


o 




< «» 


<_> 


OD 


oo a 


r* 


<o 


CM 


00 


-c 


»r 


CM 


m 


CM 


i-i 


O 


O 


•«■ 


a 


-i 














■H 






















UJ 


a. O 


































oo 


00 


oo z 


































oo 


-J 


«- 3 




OO 


-0 if 


vO 


-^ 


oo 


r- 


CM 


if 


ro 


m 


o 


o 


m 


If 


4 




O U 


_J 


in 


<o r- o 


■ft 


00 


cr 


P- 


a 


en 


in 


o 


o 


m 


1*1 


X 


00 


a 


< o 


o 


4 


r-- 


p- 


e\ 


o 


«r 


Cl 


I-* 


m 


U1 


vl 


ro 


r- 


c*> 




— 


UJ o 


3 « 


f 


■* 


r- 


l» 


o 


oo 


•♦mo 1 


<r 


o 


CI 


if 


LO 


U! 


I 




> 


0- oc 


N 


<Nj O 


a 


•-* 


r-l 


f«- 


o * <r 


r-l 


<o 


ac 


0L> 


fT| 


o 


> 


M CJ 


U U 


• 


1 


# 


t 


• 


t 


» 


• 


t 


t 


t 


• 


* 


• 


• 


«i 


r-" 


•- z 


4 


00 


00 o- 


r- 


« 


CM 


ao 


•c -t 


ft 


cn 


CM 


r^ 


o 


o 


LU 


|M 


< < 














r-l 






















O 


_i 


































LL 


o 


UJ «/) 


































O 


-J 


a vo 




00 


•o 


<0 


if 


43 


If 


If 


o 


CM 


in 


if 


<* 


m 


^f 


CD 




UJ 


< 




•*■ 


00 


4 If! O 


a 


J 


o 


r- 


r- 


P4 


Ifl 4 


00 


If 


> 


> 


X X 


o 


o 


4 If. 


>o 


O 


00 


* 


w~* 


if 


o 


o 


r- 


CM 


ft 


Ifl 


►- 




3 


o < 


r- 


4 o 


h- 


<o 


<»■ 


a 


r- 


(T| 


«t 


CM 


■ct 


•O 


<C If 


■_< 


c 


X 


Z a 


N 


«M 


(M 


a> 


•-H 


cm r- 


nO 


LTl 


o 


r-^ 


C 


OD 


00 


fO 


8 


z 


** 


a 


t 


• 


• 


• 


• 


# 


• 


• 


• 


• 


t 


t 


• 


• 


• 


3 


X 




00 


00 


&• r- 


o 


CM 


oo 


o 


>» 


CM 


ro 


CM 


r-l 


o o 


_j 


o 


< 














t-t 




















UJ 


ac 


a. 


oo • 

oo c 
































> 
1 


O 
1 

CM 




< z 


VM 


CM 


n 


•t in 


ft 


CM 


m 


^t 


Ifl 


■M 


CM 


PO 


-* 


Ifl 


UJ 


UJ 




X 
































oo 

4 

u 


oo 

4 
O 



• UJ 

oo 
uj z 
ac 4 
ll ac 



108 



00 
CO 
CD 
-Q 



+-> 




c 




<v 




c 




o 




CL 




E 




o 




o 




CO 




1 




r> 




o 


1 — 


*d- 


o 


cx» 


• 


t— 






II 


cu 


<tf> 


^ 




CO 




3 


• 


cr 


c 


jr 


o 


4-> 


• 1 — 


s- 


+-> 


fT3 


3 


LU 


p— 




o 


o 


CO 


s- 




+-> 


C 


£Z 


o 


cu 


■t-" 


c_> 


4-> 




rO 


r— 


s- 


LU 


Or 




CD 


o 


+-> 


4-> 


C 




I— I 


s 




C\J 


4-> 




O 


E 


CD 


O) 


s- 


+-> 


"r— 


to 


Q 


>> 




CO 




M- 




O 




CD 




00 




c 




o 




Q. 




(O 




<u 




on 







(_> 




fM 


o pg p- o <» 


•* #■* r- o «vj 


pi 00 P» O P- 






PI 






r- gs cr m cp 


0" CP «© Pg O 


p-l ^■ 


NNH 






-J o 




LU 


•-i eg pg cr r- 


p- eg •"■• pi pi 


-< o 


o o o 






3 ~ 




«/> 


oro^OO 


O O O O o 


o o 


o o o 






< p- 




< 


o o o o o 


o o o o o 


o o o o o 






oc < 




u 


• « • • • 


• t • • • 


• • 


• • • 






a 

>■ 

1 o 

z 






o o o o o 


o o o o o 


o o 


o o o 




















t/> 


oc ~ 




pi 


ff wono 


«l»0*l r 


— gp 


m oo go 




LU 


4 a. 






-cm •omr. 


m * O * P0 


pg >J> 


NrHH 




pi 


LU z 




UJ 


m o •-* oo r- 


O- (<1 N H - 


H O 


o o o 




p- 


z < 




1/) 


m pg pi o O 


o o o o o 


o o 


o o o 




tt 


— o 




< 


o o o o o 


o o o o o 


o o 


o o o 




LU 


_J 




u 


• • • • # 


• • • • • 


• t 


• • • 




a. 
o 
a 

a 








o o o o o 


o o o o o 


o o 


o o o 






t 




CP <*• CP fPi m 


in pg gr cr pg 


4- -0 


cp m o 




_j 




o </> 


r- f- pg o- o 


o o o o t- 


in sC 


^•ClO 




4 




UJ 


a. 


<-* O ~i O P- 


p- •* in cp cp 


p- -o 


ir> pg oo 




Q 




or. 


<_> 


IOOOITh -t 


^- p- p- m t-i 


O IT 


«j> gj •* 




O 




u_ 


«* 


OO HIMN 


in -o - * cr 


m o 


— a- <£ 




X 








• • • • • 


t • • • t 


t • 


t • t 


LU 










o o o o o 


o o — pi — 


Pi "t 


p- cr — 


O 





Q O 


























o 






O Z 


l-< PJ 


PI •<) 


in 


f-« 


<v 


m 


<f 


in 


pi pg 


n 


>» 


in 


< 






X 


C5 

< 


























or 

a 

LU 

I 






V. 


ec 


•o •■* 


•o o 


m 


pg 


IT 


■4- 


f- 


J- 


tr\ -^ 


in 


o 


pi 








*M Q 


PJ <o 


<o in 


»-< 


in 


r- 


PJ 


in 


g? 


cp pg 


<N 


pi 


p- 


Ul 










O 00 


o- -X) 


in 


r-4 


pg ■* 


m 


•£> 


cr cp 


o 


pi 


o 


pg 






LU 


-I 


ro in 


o oo 


•— t 


o- 


CP 


a 


pj 


m 


cp 0- 


o 


© 


o 


•— 






1/) 


< 


a- cr 


O CP 


o 


CP 


CP 


o- 


o 


O 


CP CP 


© 


o o 


a 






< 


3 


• • 


• • 


• 


• 


• 


• 


t 


• 


• • 


t 


• 


• 


< 






o 


O 

< 


o o 


— o 




o 


o 


o 




pg 


c o 


^1 


pi 


pi 


LU 

z 
-1 




U. 




O 


























o 




o 


•v 


< 


p- 4- 


>© CP 


pg 


pg 


fp, 


oo 


p- 


* 


m rg 


f 


o 


CI 


\- 




l/> 


f-4 


oc 


CM <> 


cr »- 


CO 


pg 


t— • 


in 


o 


n 


m oo 


X 


r- 


(Pi 






z z 




a 


PJ rr> 


pg cp 


p- 


00 


o- 


o 


■c 


03 


O CP 


O 


H 


pi 


o 




o o 


LU 




^- P- 


-i CP 


#— i 


oc 


00 


a 


r-t 


gj- 


O CP 


o 


o o 


LU 




i/> pi 


1/) 


_i 


<y a> 


O CP 


o 


a 


a 


a 


o 


o 


O CP 


o 


o 


O 


I/) 




~ »- 


< 


< 


• • 


• • 


• 


• 


• 


• 


• 


• 


• • 


• 


• 


• 


3 




0C 3 


O 3 


o o 


r- O 


«-l 


o 


o 


o 


•—I 


pH 


-4 O 


w ^ 


pi 


pi 






i -1 




i- 


























l>0 




a. o 




u 


























M 




X uO 




< 






























o 






























P> 




<_> 


>» 




























X 






o 




^ 00 


O fO 


<o 


~o 


LO 


oo 


■— t 


in 


p-i m 


^g 


< 


•a 


UJ 






4 


o 


P- fvj 


oo in 


m 


p- 


CP 


o 


p- 


<0 


CP pi 


pg 


o 


Pg 


—i 






OC 


< 


od ro 


m m 


CP 


•-* 


00 


f\J 


o 


CP 


pi C- 


Ps) 


•-1 


pi 


03 


LU 




o a 


>» <y 


pg cp 


CP 


CP 


00 


-o 


rn 


o 


CP CP 


a- 


o- 


cr 


a 


O 






Q 


(T 00 


OO 00 


OO 


CP 


a- 


CP 


a 


CP 


CP CP 


o- 





CP 


a 


QC 




-j 




• • 


• • 


• 


• 


• 


• 


• 


t 


• t 


• 


• 


• 


a 


O 




« 


O 


O O 


o o 


o 


o o 


o o 


o 


o 


o 




u. 




3 Z 


























o 






1- 




























< 


o 




U 




























Of 


<t 




< 




























o 

4 


ac 
O 

LU 








p. m «r <o 


«* 


o 


P-4 


p- 


in 


00 


O o 


•c 


fM 


»-4 


3 


X 






P0 


O a 


oo o 


o 


pg O O 


r~ 


CP 


in gj 


pi 


P- 


g> 


t- 


p- 


z 






<*■ o 


CP <c 


CP 


V-4 


rg 


CP 


or 


•o 


pi p- 


pg 


P- 


m 


u 




LU 




UJ 


0D o 


pg pg 


CP 


o 


Pi 


IT- 


gj 


•o 


g3 pp 


1*1 


pn 


p- 


< 


UJ 


UJ 


o 


«/) 


rp m 


— fi 


(^ 


in 


m 


IT 


p- 


pg 


g) CP 


CM 


pi 


>J- 




PJ 


X 


< 


< 


• t 


• • 


• 


• 


• 


t 


• 


• 


• • 


* 


• 


• 


z 


PI 


p- 


oc 


U 


oo cr 


O 00 


gs 


n 


o 


p- 


in 


ro 


fo pg 


(Nj 


i-i 


O 


1-4 


oc 


UJ 


a 






— -4 




r-4 


f-t 


















< 


03 






























o 


Ul 


p% 


oc 




























LU 


z 


P- CO 


< 




cr in 


o o 


in 


pM 


o 


00 


-0 


r-4 


gj p- 


sC 


o 


o 


»- 


PI 


Z UJ 


UJ 


fl-4 


P0 CP 


o r- 


f> 


pg 


-* 


o 


m 


m 


g> m 


^ 


^ 


p- 


3 


_l 


UJ X 


z 




pg pj 


m pg 


m 


« 


-^ 


•-H 


in 


p^ 


fp| a 


rg 


00 


fpi 


& 




X U 


h— 


LU 


CP m 


<C tr\ 


•^ 


in 


oo 


p- 


r~i 


g/ 


gi ro 


m 


l«l 


r- 


X 


o 


uj z 


_J 


V> 


-# <o 


— gp 


<»■ 


gf 


(M 


u\ 


P- 


pg 


<* CP 


pg 


pg 


>»■ 


O 


*- 


O N- 




< 


• t 


• • 


• 


• 


• 


t 


• 


• 


• i 


• 


• 


t 


(J 




< «- 




u 


0D O- 


O OO 


-o 


fri 


o 


r- 


m 


rn 


m pg 


pg 


^* 


o 


«p 


o 


_i 








.-« 




pH 


pg 


















LU 


a a 






























i/> 


1^ 


ts> z 






























l/l 


3 


■- 3 






00 Psl 


•» pg 


•* 


pg 


p-i 


ao 


m 


>*■ 


in cr 


O 


o 


p- 


< 




a lj 


-J 




m pg 


cp m 


^-* 


<o 


■g 


o 


CP 


ao 


P- 00 


•c 


>!• 


o 


X 


i^ 


oc 


< 


c 


pg i-i 


pg cp 


•»• 


<ti 


p- 


«", 


>» 


pH 


pg cr 


o 


>U 


ro 




— 


LU O 


3 < 


•-< f-< 


m n 


o 


^- 


a 


* 


P0 


LP 


gj rn 


rn 


rn 


r>- 


X 




> 


»- 


oc 


O CP 


o «»■ 


fl 


<0 


rn 


-o 


o 


O 


>»• CP 


pg 


•-1 


•f 


u 


> 


•-> u 


«_> 


CJ 


• t 


• t 


t 


• 


• 


• 


• 


• 


• • 


• 


• 


t 


^ 


r" 


p- z 


OL 




o> CP 


O 00 


<u 


(*« 


o 


p> 


in 


m 


fi pg 


rg 


,— t 


o 


UJ 


pi 


4 < 








—> 




•-< 


pg 


















U 


_i 






























u. 


O 


UJ f> 






























o 


-J 


oc «/) 






O pg 


<C P- 


p^ 


fPi 


a 


* 


pg 


pg 


oo go 


gr p- 


m 




UJ 


4 






m (*> 


fP> o 


O 


P- 


m 


m 


P- 


cr 


CP pi 


m 


•c 


pg 


> 


> 


X X 




o 


o> m 


v •* 


oo 


CP 


m cp 


rn 


00 


Cr C 


ao 


>D 


p- 


K 




3 


O < 


a CP 


■4- pg 


o 


eg 


p-4 


m 


s» 


CP 


00 -C 


>1 


•* 


r- 


». 


a 


X 


z 


oc 


<*■ o 


•■• •* 


O 


r»- 


m cp 


o 


f^ 


^- CP 


pg 


pi 


gr 


u 


z 


PI 




o 


# t 


• t 


• 


• 


• 


t 


1 


t 


• • 


• 


t 


• 


o 


3 


X 






LP —. 


pg cp 


P- 


ro 


O P- 


~o 


m 


pi pg 


pg 


p* 


o 


—1 


o 


< 






pg 


•-" 




^g 


p-t 
















LU 


ec 


X 


l/l 


• 


























> 
1 

Pi 


O 
1 

pg 




<<o O 
































4 Z 


rH pg 


m <t 


m 


pg 


pg rri 


gf 


m 


pg pg 


in 


•*• in 


LU 


LU 




X 




























«>0 

< 


4 

o 



• UJ 

a o 
uj z 

0C 4 
U. ct 



109 



U PJ 

JO uj 
3 •-• oo 

OC < CJ 

o a 

> 
i o 

z 

OT •— »-l 

uj < a 

— UJ X tu 

*- Z < OO 

OT ►- O < 

uj _j o 

a 

o 

a. 

a. 



on 



< 
O 

O 



o oo 

uj a. 
ot o 



+J 

E 
d) 
E 
O 
Q. 
E 
O 

o 



O Co p- O ■* 

r» *c o* CO C* 

dNHOO 

o o o o o 

• • t • • 

o o o o o 



-* O O -O _i 

oo r» o ■* m 

pj m a 03 in 

<*■ -< o o o 

o o o o o 

• • • • • 

o o o o o 



o* or u* co m 

p» p- po a> o 

t-» OS t-< O p- 

po 00 m tart .4- 

OOrtNM 

• • • • • 

o o o o o 



♦ rlf-ON 

» ff -ONO 
P» PO «-< tart tart 

o o o o o 

o o o o o 

# • • • • 

O O o o o 



«d m or o oo 

VJMhhO 

o o o o o 
c o o o o 

* • t • • 

o o o o o 



ir. cm •>»■ a- po 

O O 03 O P- 

p- .4* m o> a 

«»■ p- r- co •-! 

<vi <o •-• oo o- 

• • • • • 

O O *-> t-< w-> 



^ oo p- o p- 

PO >» PJ CM tart 

•-< o o o o 

o o o o o 

o o o o o 

• • • • • 

o o o o o 



O <f IT- 0C (Ti 

•— OT <M tart tart 

•10000 

O O O O O 

o o o o o 

• • • • • 

© o o o o 



-4 ^) O 1 (^ O 

IA4 •* CIO 

■-< O If. (V oc 

o <r •* oo o 

m o —> o- -c 

• • • • • 

—i or r- a r-. 





"in 




o o 




"d- • 




en 




r— II 




« CO 




ai ca 




-i<£ 




fO 




3 • 




cr e 




-E o 




-M T- 


en 


s- +J 


• 


ra 3 


CO 


UJ r— 




o 


CD 


o oo 


p— 


S- 


.Q 


+-> E 


ra 


E O 


I— 


CL> -i- 




O +-> 




03 




i— S- 




uj o> 




a> 




O -M 




+■> E 




1— 1 




s: 




C\J 4-> 




o 




E a> 




<L) S- 




+-> •!- 




CO Q 




>> 




CO 




<4- 




o 




aj 




co 




E 




o 




Q. 




CO 




a> 




a: 





a 


O 


























o 






o z 


frt PJ 


m <» 


in 


pH 


(NJ 


n 


>t 


m 


^ 


<\l 


p «* 


m 


<t 






X 


< 


























ot 
o 

UJ 

X 

t- 






■"V CC 


t- 0> 


c in 


u\ 


t-rt 


C7- 


in 


CO 


a 


<o o 


tart p- 


P0 








PJ o 


O sO <M 00 


00 


<*• 


O 


00 


pn 


rj 


00 


tart 


oo in 


pj 


UJ 










o* o< 


<C (j» 


p-> 


o 


CT> 


o 


o 


tart 


o- 


0(M> 


0" 


PJ 






UJ 


J 


o> 0" 


o o- 


tart 


a> 


ac 


a 


o 


«-* 


<r 


O 


o> c 


o> 


tart 






oo 


« 


o* 0» 


o o> 


o 


a 


a 


a 


o 


o 


o- 


o 


<x o- 


o- 


CC 






4 


3 


• • 


# • 


• 


• 


• 


• 


t 


• 


• 


• 


• • 


• 


< 






o 


O 

< 


o o 


-- o 




o 


o 


o 




ta-l 


o 




o o 


o 


Ul 

z 
_J 




u. 




o 


























O 




o 


"V < 


r- oo 


ro o 


p- 


r- 


oc 


pn 


ao 


<c 


0> 


p- 


o <o 


o 


K 




00 


M 


(X 


p* r- 


P- 00 


hO 


•0 


ro 


PS) 


p- 


ro 


PO 


•o 


•*- PJ 


o 






z z 




O 


O- 0> 


ro a> 


a 


CM 


,_< 


ro 


PM 


o 


o 


o o o> 


o 


O 




o o 


UJ 




o- a- 


tart o- 


tart 


rj> <f 


rr 


O 


tart 


o 


o 


o o- 


o 


UJ 




to >-■ 


oo 


-I 


0^ <7> 


o rj- 


o 


o- 


a 


a 


O 


o 


o 


o 


o o- 


o 


O0 




►- H- 


< 


< 


• • 


• • 


• 


• 


• 


• 


• 


• 


• 


• 


• • 


■ 


3 




or r> 


u 


3 


o o 


tart o 


,— i 


O 


o 


o 


,~t 


»-rt 


tart 


Ptal 


-• o 


ta-» 






< _j 




*- 


























oo 




Q. o 




l_) 


























tart 




X oo 




< 






























o 






























ta^ 




u 


«v 




























X 






(9 




0> -rt 


00 INJ 


<o 


PJ 


w—t 


<0 P- 


a 


tart 


pH 


p- r- 


<» 


UJ 






< 


O 


o> o 


<t) -rt 


a 


CO 


PA 


o> 


in 


o- 


PJ 


in 


««o 


—1 






ae 


<. 


o> o 


o- o 


p- 


fn 


~t 


^ 


pj 


PO 


«t 


P0 


po po 


PJ 


OD 


UJ 




O 


a 


o> o 


■O O 


<o 


a 


a 


a- 


00 


IT- 


<r 


o- 


(r o> 


o> 


o 


u 






O 


o> o 


fjs O 


o> 


0> 


a 


o- 


a 


a> 


a 


o- 


o> CJ> 


0> 


a 


or 




_i 




• • 


• 9 


• 


• 


• 


f 


• 


• 


• 


• 


• • 


• 


a 


o 




< o 


O tart 


o >-< 


o 


o o 


o 


o 


o 


o 


o 


O O 


o 




u. 




D Z 


























o 






h- 




























< 


c 




U 




























or 


«I 




< 




























a 

_j 


or 

Q 
UJ 








er\ 00 


P- o 


>!■ 


PO 


r/i 


p^ 


CD 


pj 


•* 


,.. 


rr p- 


00 


3 


X 






r\i 


f- re 


•* PO 


P>J 


<» 


o~ 


>» 


pn 


p- 


<c 


•£ 


<\i tart 


oj- 


ta- 


t- 


z 






►- CM <M -0 


ITi 


o 


CO 


ta- 


CO 


pj 


i-rt 


O 


o m 


PJ 


O 




UJ 




UJ 


•O * 


00 P- 


* 


m 


nI" 


in 


in 


p- 


o 


Pi 


m m 


m 


< 


UJ 


UJ 


o 


oo 


CM P0 


o> 0" 


O 


o 


vO 


in 


-J- 


c 


t-4 


JD 


ao oo 


pn 




KJ 


X 


< 


< 


• • 


• • 


• 


• 


• 


# 


• 


• 


• 


■ 


• • 


• 


z 


M. 


►- 


tc 


u 


oo ao 


oo r» 


<o 


PJ 


00 


vO 


«f 


tart 


PO 


PJ 


•-I o 


O 


tart 


or 


UJ 


a 










tart 




















<i 


CD 






























o 


UJ 


^ 


a. 




























UJ 


z 


1- 00 


< 




•o m 


00 P- 


o 


fjs p- 


o 


p- 


ta" 


o 


(M 


P- ,o 


m 


t- 


tart 


rtT UJ 


UJ 


f-4 


te\ tai 


oo rri 


a- 


00 O 


r\i 


o 


•o 


PO 


tart 


PO P- 


p- 


3 


-1 


UJ X 


z 




oo rn 


00 <o 


c* 


P» 


a 


pn 


a 


rrt 


ro 


r-j 


tart ir\ 


pj 


a 




X (J 


tart 


u. 


O «» 


<» p- 


p- 


P- 


<C 


p- 


o 


00 


O PO 


in m 


m 


X 


o 


uj z 


_l 


oo 


<M (N/ 


O <?> 


<~> 


o 


>o 


in 


>r 


0> 


tart 


o 


ao ao 


PO 


o 


f- 


<_) "- 




« 


• t 


• 


• 


1 


• 


« 


• 


f 


• 


• 


• • 


• 


o 




< — 




o 


00 00 0* f*" 


<o 


PJ 


OD 


*o 


-»■ 


tart 


PO 


PM 


ta- O 


o 




o 


J 












*-* 




















UJ 


a. o 






























oo 


oo 


oo z 






























00 


_> 


•- 3 






CO tart 


m pj r- 


V 


PJ 


oc 


CO 


tart 


CJ> 


m 


^- (p 


m 


< 




CJ u 


-J 




s? 


rr, \r\ 


-0 


o 


<»■ o> 


<0 


P- 


o 


PO 


<C PO 


p- 


X 


oo 


a 


< 


o 


<o p- 


C4 


p- 


* 


p- 


<0 


ff> 


Po O 


O •O 


CM 




•-< 


UJ O 


3 < 


r>- ^- <M r- 


-o 


■0 


-r 


p-rt 


in 


•r 


o 


PO 


m m 


m 


X 




> 


o- 


ox 


rj eg 


a> o> 


o> 


•-rt 


p- 


rtJ 


>*■ 


o> 


tart 


NO 


0D 00 


po 


U 


> 


•— i_j 


u 


u 


• • 


• t 


• 


• 


• 


• 


t 


• 





• 


• t 


t 


<l 


P- 


K- Z 


«1 




ao oo 


00 p- 


ITi 


CM 


00 


■4i 


>»■ 


tart 


ro pg 


tart o 


o 


UJ 


tart 


< rt* 












*-4 




















u 


J 






























u. 


o 


UJ OO 






























C 


-J 


0C 00 






OO ,© o IT. 


«3 


in m 


po 


in 


m 


>t 


po or 


ao 




UJ 


< 






<* CO 


<#■ IT. O 


rj» 


N* 


rtJ 


p- 


r» 


tart 


in 


•JJ- au 


m 


>- 


> 


X X 




o 


o vj- irv *o o 


00 «!■ 


r-« 


m 


ro 


o 


p- 


P0 — . 


in 


ta- 




3 


o 


4 


r- ^ o r» «0 


* 


rj^ 


P- 


pn 


^ 


PJ 


4- 


<0 03 


m 


t-4 


a 


X 


Z ec 


PJ «M 


pj ep 


tart) 


pj 


p- 


>o 


m 


o 


tart 


■* 


00 CC 


PO 


u 


z 


tart 




o 


• • 


• t 


• 


• 


• 


• 


• 


• 


t 


• 


• • 


• 


o 


3 


X 






ao oo c r* 


-0 


PJ oo <o 


-t 


pj 


PO 


pj 


tart o 


o 


-1 


o 


< 












tart: 


















UJ 


ox 



oo • 

oo O 



• UJ 

o o 
uj z 
or < 
u. or 



»rt po po ^- in 



-< po ro or m 



tart P0 PO S 


r in 


ai 


UJ 






00 


oo 






•«* 


< 






o 


u 



no 





+J 




c 




ID 




C 




o 




Q- 




E 




O 




O 




co 




1 

2: 




« r— 




o o 




^- • 




C7> 




i— II 




■ 




a> ca 




J*i 




(O 




3 • 




O" c 




-C o 


o 


+J -I- 


1 — 


s- +-> 


• 


rC 3 


CO 


LU i — 




o 


<L> 


o co 


i— 


S- 


-Q 


+-> c 


rC 


c o 


1— 


aj -r- 




O 4-> 




fO 




r— i. 




UJ CD 




a> 




O 4-> 




+-> c 




1— 1 




_l 




CO +-> 




(J 




E <U 




a> s- 




+-> '1- 




tO Q 




>> 




CO 




4- 




O 




a> 




to 




c 




o 




Q. 




to 




a> 




C£ 





u 






OJ 


-* o> 


r» tn 


r- 


r- fO ft m fn 


If o O to <M 






*- 








in ao 


in O 


o- 


ffCOMfh 


O CO 


OJ _• 


f-4 






_l 


a 




UJ 


.-" o> 


>o in 


ro 


m -» ** © o 


o o o o o 






=> 


•— < 




1/1 


«N O 


o o 


o 


o o o o o 


o o 


o o 


o 






< 


►- 




« 


o o o o o 


o o o o o 


o o o o 


o 






a. 


< 




o 


• • 


• • 


• 


• ••ft 


• • 


• • 


• 






O 

>• 
X 


a. 






o o 


o o 


o 


o o o o o 


o o 


o o 


o 






O 


























2 






















</> 


oc 


*- 




^* 


«* >*■ 


4- <o 


— 


^ M M/\ ^ 


CO ft 


O oo 


o- 




UJ 


< a 






oo r- 


~ o> 


ft 


.*• <» oj r- <*"> 


*0 OJ 


00 ,c 


■4- 




*— 


UJ 


X 




UJ 


.O h- 


m c\ 


•O 


^ n <m h »< 


OJ ft 


o o 


o 




•- 


z 


<s 




to 


** o 


o o 


o 


o o o o o 


o o 


o o 


o 




oc 


■— 


c 




< 


o o 


o o 


o 


o o o o o 


o o 


O O 


o 




UJ 


-J 






o 


• • 


• • 


• 


• • • • • 


• t 


• • 


• 




a 
o 
a. 
a 










o o 


o o 


o 


o o o o o 


o o 


o o 


o 








9 


■ 


o> ao 


m + 


m 


tO C- O CD 00 


4- -0 


to r~ 


*• 




_j 






CT 


to 


to — 


OJ O 


o 


O co <C m to 


in oj 


•O oj 


ao 




< 






LU 


a 


in c- 


c* ^ 


r~ 


f— r- <c >-> oo 


<-* <o 


* o 


in 




o 






a. 


u 


^ a 


■* a 


st 


<f ClOlM" 


o o 


•-< a 


<T\ 




o 






u. 


»- 


o o 


ft ft 


OJ 


OJ to 00 O CO 


to OJ 


0" fo 


*+ 




X 










• ♦ 


• t 


• 


• t • • • 


• • 


• • 


• 


LU 












o o 


o o o 


O O O — i — i 


ft CO 


»* <c 


ao 


l_> 
o 








UJ • 

o o 
















LL 








o 


z 


•-" OJ 


CO ■# 


to 


w-> oj rr ^ to 


—1 OJ 


ro >*■ 


to 


< 








X 


















o 







o 


























X 








<[ 


























1- 






X. 


oc 


u\ 


•-< 


* r- 


o 


r-* t-4 


OJ 


•J 


ft 


CO o> 


ft 


•£ 


»-« 








OJ 


a 


OJ f- 


ao r- 


* 


■* •»■ O to 


o- 


o o 


o 


CO 


ft 


111 










-*■ 


•4- 


ft a 


OJ 


03 0~ 


to o 


to 


<c o 


>»■ 


o 


in 


KJ 






LU 


-J 


ao 9 


ao cc 


•0 


O oj 


to 


U~ 


in 


ao co 


a 


o- 


•0 


ft 






(/> 


« 


o 


a 


o- a- 


o> 


O O 


o 


O 


o 


o o 


o 


o 


o 


a 






< 


o 


t 


• 


• t 


• 


• • 


• 


• 


• 


• • 


• 


• 


• 


< 






o 


t- 


o o 


o o 


o 


f i-i 


r~i 


ft 


ft 


ft ft 


ft 


ft 


»-l 


UJ 








tj 


























z 








< 


























_J 




U, 




o 


























o 




o 


^v 


< 


a 


OJ 


fl ~o 


o 


.J- tri 


CO 


Ol 


o 


OC OJ 


OJ 


■£> 


0* 


1- 




tr> 


■H 


a 


|H| 


•o 


a oo 


<o 


o cr 


CC 


to 


r~ 


0- 00 


•o 


OJ 


ft 






z z 




o 


st 00 


« m 


»»■ 


h- oo 


ro 


r» 


OJ 


—i -JO 


&■ 


<0 


<o 


o 




o o 


UJ 




0- 


o 


w o> 


ao 


0> O ft o 


ft 


o o 


o 


o <* 


UJ 




1/1 .- 


V) 


_J 


cr 


o 


a> a 


C7> 


o> o 


o o 


o 


o o 


OOff 


to 




►- K 


< 


< 


• 


• 


t • 


• 


t • 


• 


• 


• 


• • 


• 


9 


• 


3 




a o 


t_> 


r> 


o 


•— * 


o o 


o 


O ft 


-H 


ft 


•-^ 


ft f 


r-i 


ft 


o 






< -1 




t- 


























to 




o- c 




u 


























HI 




X <S> 




< 






























o 






























^N 




u 


•v 




























X 






o 




t-H 


fl 


«t o 


o 


ro o> 


r- 


o 


o 


to r~ 


oo 


IT, 


m 


UJ 






< 


o 


to 


OJ 


r- to 


* 


CD o- 


r* 


a 


to 


0* CO 


OJ 


<0 


to 


-J 






C£ 


< 


ao 


m 


— <o 


><■ 


o o 


■J- 


sO 


OJ 


co to 


o- 


f* 


r~ 


ao 


UJ 




q a 


<o 


m 


r- * 


ro 


o- <0 


o 


o 


o 


0- cr 


co 


a 


t— * 


O 


<-> 






o 


<r 


a 


0- o~ 


a> 


<T (T 


0^ 


a 


o- 


CO 00 


ao 


oc 


0- 


cc 


oc 




-J 




• 


• 


• • 


• 


9 • 


■ 


• 


t 


• • 


• 


• 


• 


a. 


o 




< 


o 


o 


o 


o o 


o 


o o 


o 


o 


o 


o o o 


O 


o 




u. 




3 


z 


























o 






>- 




























< 


o 




o 




























oc 


< 




•< 




























Q 

< 


cc 

o 

UJ 








to 


o 


fo O 


OJ 


oj O 


a- 


to. 


tO 


o >o 


o 


ft 


CC 


3 


X 






OJ 


OJ O 


Ov o 


m 


r- oj 


o 


•» 


o 


to O m 


O 


•■0 


H 


t- 


z 






r- 


00 


ao in 


ro 


ft oo 


■£> 


^H 


^J- 


r- O 


o 


a- 


r>- 


l_> 




UJ 




UJ 


eo 


rr\ 


<c o 


fO 


OJ OJ 


OJ 


r» 


00 


a o- 


r- 


o 


OJ 


< 


UJ 


LU 


o 


to 


in 


4- 


ao to 


to 


~t> tSi 


f^ 


ro 


r^ 


cr >» 


fO 


r- 


f-< 




M 


X 


< 


<. 


t 


• 


• • 


# 


t • 


• 


• 


• 


# • 


• 


• 


• 


Z 


l_t 


►- 


tx 


u 


OJ 


O 


O ao 


<c 


o to o 


r~ 


>» 


•c to 


-t 


OJ 


ft 


** 


oc 


UJ 


a 




!-< 


•— i 


ft 




ft ft 


ft 
















< 


00 






























o 


UJ 


^ 


oc 




























UJ 


z 


H 1^ 


< 




h- 


a 


o- <?■ 


o 


o r- 


to 


to 


r- 


vO <o 


CO 


m 


ft 


f- 


M 


Z UJ 


UJ 


^^ 


«» 


cr 


ci o 


00 


oo 00 


CO 


to 


au 


« n 


t-1 


tr 


t- 


3 


fl 


cu x 


z 




* 


ro 


o o 


ft 


<o OJ 


r» 


a 


CO 


m -f 


It] 


00 


■*■ 


a. 




x o 


fc-t 


UJ 


^4 


ao 


00 >t 


ao 


■O ft 


o 


•« 


au 


m co 


m 


o 


m 


X 


o 


UJ Z 


-J 


to 


r- 


to 


o» to 


<o 


•* o 


ro 


o 


m 


«» O 


o 


<»• 


o 


o 


►- 


o ■— 




< 


• 


# 


• t 


• 


• • 


• 


• 


• 


t • 


• 


• 


• 


u 




< — 




u 


OJ 


o 


O 00 


-o 


•e to O r- •* 


•C in 


^- Ol 


^ 


•» 


o 


— 1 






f-H 


r-< 


ft 




ft f t 


f* 
















tu 


a u 






























oo 


tn 


»0 Z 






























to 


-j 


— 3 






ro 


M\ 


OJ 00 


«— » 


f ft 


V 


o- 


OJ 


O 9- 


•* 


co «jr 


< 




o o 


-J 




r- 


tn 


(jx 00 


CO 


ao o- 


<c r- 


CO 


C 00 


r- 


Ol 


r» 


X 


</> 


a. 


« 


o 


00 


tr\ 


0» OJ 


43 


m o> 


<o 


>o 


ff 


CM st 


-»• 


m 


00 




h* 


UJ o 


3 


4 


00 


a- 


•c a 


ao 


ft r- 


■0 


^-( 


m 


-r m 


e'- 


cc 


m 


X 




> 


1- 


s 


r» 


-«• 


o «. 


r- 


m ao 


^H 


o 


m 


«r o 


er 


•»■ o 


o 


> 


— u 


u 


# 


• 


• • 


t 


• t 


t 


t 


• 


• « 


• 


t 


• 


4 


r— 


►- z 


4 




OJ 


o 


■-I 00 


•o 


<o ^> 


a 


r- 


* 


<o m 


CO 


rsi 


ft 


UJ 


f* 


< < 






m\ 


f-t 


ft 




t-< •-< 


t-^ 
















U 


_l 






























LL 


o 


UJ <Si 






























o 


-J 


a <s> 






00 


»o 


ft *- 


ao 


-C * JJ 


CO 


<o 


m oj 


<M 


tr 


o 




UJ 


4 






^ 


to 


o» >o 


r- 


tr oo 


<M 


r- 1 


or 


OJ •» 


f i 


f\ 


<r 


> 


> 


X X 




o 


* 


HON 


« <*i 


-f 


r- 


o 


f- OJ 


OJ 


to 


fO 


1- 




3 


o 


< 


o •* o- o 


«0 


t-H OP 


fO 


n 


OJ 


O «t 


o- 


CO 


to 


ta- 


Q 


X 


Z a: 


oj oj ro ao 


OJ 


o «» 


OJ 


r» 


o 


oj *o 


•t 


r» 


»~l 


u 


Z 


** 




a 


• 


• 


• t 


f 


• • 


• 


• 


# 


• 9 


9 


• 


• 


o 


3 


X 






«*» 


•-I 


ft ao r- 


h- in 


r-t 


r- 


m 


p~ m 


•* 


CM 


r-< 


-J 


O 


< 






<-• 


■-I 


M 




ft ft 


ft 














UJ 


oc 


X 






























> 


o 



1^ • 

in O 

< z 



• UJ 

a u 

UJ z 
cc < 
u. oc 



h n r, ^ in 



— i oj ro ^ in 



—i oj ro ^- in 



< 



Ill 



+-> 

c 

ID 



O 

Q. 



O 
O 



CO 





u 






CM 


•- c p». m p- 

in e it O V 


a od (m cr r- 


m o o m cm 

O CI CM r-t w-> 






-1 o 




UI 


rt»<Kl^ 


Cl --) r-t o o 


o o o o o 






3 


t-4 




«/) 


CM o o o o 


o o o o o 


o o o o o 






< 


i— 




« 


o o o o o 


o o o o o 


o o o o o 






a 


< 




o 


• • • • H 


t • • • • 


t • • • t 






a. 
> 

1 O 






o o © o c 


o o o o o 


o o o o o 






















z 














«/) 


ec 


tart 




r-t 


<e «m p- p- o 


r-t ^ CM ITl OC 


Nir^ci « 




Ui 


< a. 






Cl CM * <0 — i 


f> <■ 4) cm a 


.*• <C + Cl CM 




tart 


uj x 




UI 


<-• ITt Cl IM CM 


IANHHO 


~* o o o o 




»- 


z 4 




to 


-< o o o o 


O O o o o 


o o o o o 




cc 


•-• 


Q 




< 


o o o o o 


o o o o o 


o o o o o 




UJ 


_i 






l_> 


• • • • • 


t • t • • 


• • • » • 




& 
O 

(X 
0- 










o o o o o 


O O o o o 


o o o o o 








• 


_ rv 


CP CC Cl * m 


IACOCK 


^ <o ir » 4° 




-1 






a to 


ViHNOO 


O ci «o ci in 


m CM -0 CM 0D 




< 






UJ 


a 


mCff 4N 


^ P- 00 »- 00 


—• o <r O in 




o 






a 


u 


-»• a ■* a «r 


■f noir m 


o «o »-< <p ci 




O 






u. 


rt* 


O O ft --< CM 


Minoom 


IflNO 1 WH 




x 






LU 

o 


• 

o 


• • • • • 

o o o o o 


• • • • • 

O O O tr* r-t 


• • • • • 
•-< O <4 O 00 


UJ 

(_> 

OC 

o 

u. 

o 








o 


z 


•i cm ci >* m 


»-' CM Cl ■* m 


-* <M r i -* m 


<l 








x 










Of 

Q 





•> in 




o o 




«vT • 




CXi 




i— II 




« 




cu ca 




_-_ 




CO 




3 • 




a- c 




-C o 


r— 


+-> >i- 


1 — 


s- +-> 


• 


CO -3 


OO 


LU i — 




o 


a> 


o co 


r— 


i- 


-Q 


+-> c 


to 


c o 


\— 


<L) -i- 




CJ +-> 




fO 




r— S_ 




UJ CD 




a> 




O 4-> 




4-> C 




1— 1 




_l 




0O -l-> 




<_> 




E CD 




cu s- 




4-> •.- 




to o 




>> 




CO 




M- 




O 




CU 




to 




c 




o 




Q. 




10 




O) 




cc 







o 




























I 








< 




























1- 






^> 


OC 


CM CM 


(V 


m 


<o 


CI 


w-t 


r-» 


o 


CM 


•*■ 


<M 


P- 


nO <o 








CM O 


t^ un 


o- 


a> 


IT 


m 


CM 


—i 


in 


•» 


CO 


in 


P- 


<C f- 


Ul 










o r- 


oo 


o- 


O 


m r^ 


t- 


•c 


CD 


Cl 


CI 


Cl P- f^ 


KJ 






UI 


-J 


r~ a 


r- 


o- 


o 


O 


^_4 


■H 


O 


O 


o o o 


o o 


trt 






»o < 


o> C> 


cr 


0- 


o 


o O 


o o o 


o 


O 


o 


o o 


or 






< 


rs 


• • 


• 


» 


• 


• 


t 


• 


• 


• 


• 


« 


» 


• • 


•< 






o ♦- 


o o 


o o 


r-l 


H 


r-l 


•-< 


^^ 


r-t 


r-t 


r-t 


r-t 


r-t f< 


UI 








u 




























z 








< 




























•—1 

-J 




IX. 




o 




























o 




o 


"s. 


< 


4- a- 


oo 


m ci 


CM O 


t-l 


CM 


o 


t~ 


•* 


r-t 


CM O 


»- 




(/> 


W* 


a. 


CM 00 


f- 


a 


CM 


f^ 


CD 


>* 


o r- 


o 


00 


CM 


00 O 






z z 




O 


O f^ 


00 


<r 


o 


o 


^4 


r+ 


m 


CI 


w* 


O 


r-t 


CM Cl 


o 




o o 


UI 




o o 


0> 


a> o 


o 


— ' 


r-t 


o 


o 


o o o o o 


UI 




lO <- 


to 


_l 


o o 


cr 


cr 


o 


c o 


o 


o 


o 


o o o o o 


lO 




1— r~ 


< 


< 


• • 


t 


• 


• 


• 


t 


• 


• 


• 


• 


• 


r 


• • 


3 




a. 3 


(_) 


3 


f-i t-4 


o 


o 


•-« 


f4 


r-t 


r-t 


r-t 


r-t 


•-• 


f— * 


— t 


r-t rH 






< -1 




»- 




























<o 




a. o 




o 




























tart 




x to 




< 
































o 
































«-» 




u 


«v 






























X 






o 




r» o> 


in 


(M 


in 


CO 


IT 


CM 


<M 


O 


in 


CI 


cr 


*o Cl 


UJ 






< 


o 


■o irv 


<c 


O 


<~4 


m 


-C 


f- 


O 


O 


00 


CM 


C 


Cl Cl 


_l 






OC 


< 


* r~ 


00 


O 


o 


o> 


r» 


v0 


cr 


00 


CI 


-4 


-* 


co ao 


00 


UI 




a 


OC 


t~ <c 


r- 


o 


o 


r^ 


<a 


•o 


cc 


r- 


o- 


Cf 


cr 


oo ac 


o 


o 






a 


cr o* 


cr 


o 


o 


o> 


a 


o- 


o- 


o- 


c* 


a- 


cr 


c o> 


OC 


OC 




_i 




• t 


• 


• 


• 


• 


• 


t 


t 


• 


• 


• 


• 


• • 


CL 


o 




■< 


o 


o o o 


rM 


r-4 


o o 


o 


o 


o 


o 


o 


o o 




U, 




3 Z 




























o 






>- 






























< 


o 




O 






























et 


•< 




< 






























o 

_i 
< 


cc 

a 

UI 








f- CO 


*> 


r^ 


«» 


CM 


in 


IM 


OC 


-» 


m 


CM 


r-t 


•~> •* 


3 


X 






CM 


cm e- 


a 


Cd 


CM 


<0 


vO 


rn 


in 


00 


CI 


<c 


M 


P- ^ 


1- 


»- 


z 






O IT 


ft 


r^ 


CM 


o 


<M 


0" 


o 


r- 


r>- 


■* m 


m oo 


O 




UI 




UI 


O CM KN CI 


«* 


O in 


•* 


r- 


r—t 


r-l 


CO 


fO 


o o 


< 


UJ 


UI 


o 


to 


•O CM r» 


o 


CM 


o 


00 


r^ 


r-t 


t<- 


CM 


r-t 


Cl 


sC P- 




IVI 


■x 


< 


< 


• • 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• • 


z 


t— 


T~ 


OC 


U 


9> oo 


00 


00 <0 


m 


IM 


co 


in 


CM 


>* 


c\ 


CM 


r-t O 


N4 


OC 


Ul 


o 












pH 


r4 


















<. 


03 
































o 


UI 


M 


OC 






























UI 


z 


r- to 


< 




if\ — > 


-* 


>*■ 


<o 


a 


cr 


cr 


rsi 


C. 


r-t 


o 


in 


o a 


i- 


1-4 


Z ui 


UI 


ff-4 


O CM 


m 


in 


rl 


r- 


f-t 


p- 


r~ 


r-t 


P- 


r-t 


CM O O 


3 


-J 


UI X 


z 




r-t f-> 


o> 


r^ 


o 


r~ 


>» 


cr 


(M 


in 


m 


•o 


a 


ao m 


a 




X o 


M 


UI 


o — 


CM CI 


^ 


CI 


co 


CT 


-O 


o 


o 


r» 


<M 


o> o 


X 


O 


UI z 


-1 


</) 


CO o 


<r 


c 


CM 


o> 


r- 


o 


r-t 


r>- 


CM 


r-t 


Cl 


m p- 


o 


1- 


o ►» 




•3 


t t 


* 


t 


• 


t 


t 


t 


• 


• 


• 


• 


• 


• • 


o 




«i — 




u 


0> CD 


OD 


00 


<C 


* 


CM 


CD 


m 


CM 


-* 


f\ 


<M 


w* o 


iM> 


o 


_j 














M 


i-* 


















UJ 


a a 
































to 


to 


l/> Z 
































(O 


_> 


— 3 






v r~ 


•c 


CM 


in 


fd 


m 


cm o m 


Cl 


•f 


•4- 


i-< 00 


< 




o u 


_l 




V -< 


< 


<T 


f» 


o 


r-t 


<c 


o- 


r-t 


CM ■* 


^ 


m o> 


X 


(O 


OC 


< 


o 


00 <o 


o 


r- 


au 


r- 


m 


r-t 


o 


in 


r-t 


Cl 


■O 


Cl CM 




tart 


UI o 


3 


< 


0> ■* 


■* 


c\ c> 


CM 


Cl 


o 


m 


o> 


O 


p- 


CM 


CP o 


X 




> 


t- 


a 


t>- cm a 


O CM 


0> 


<o 


>o 


f-» 


<o 


CM 


r-* 


co 


m p- 


u 


> 


»- CJ 


u 


<j 


• • 


• 


• 


• 


• 


• 


t 


# 


• 


• 


• 


• 


t • 


« 


K 


P- Z 


« 




(|> GO 


00 


as 


•C 


•«■ 


PM 


cc 


m 


CM 


<* 


Cl 


<M 


•-• o 


UJ 


tart 


< < 














r* 


t-H 


















u 


•J 
































u. 


a 


UI <o 
































o 


-i 


ot to 






CM -O 


(M 


00 


* 


in 


<D 


CM 


m 


0> 


-t 


•o 


P- 


p. 00 




UJ 


« 






o c> ir r- oo 


CM 


m 


h- 


O 


r>- 


CM 


oo 


(M 


CM CM 


>• 


> 


X X 




o 


ci cm m r- t» 


CD f- 


r» 


CI 


in 


t>- 


r* 


O 


CM r-t 


H- 




D 


o 


< 


Cl CM 


CI 


Ci 


c 


Cl 


in o» 


0- 


in 


CM 


o- 


^ 


r-t r-t 


M 


Q 


X 


z 


a 


O in 


•-" 


O CM 


CM 


o 


00 


^h 


r~ 


CM 


r-t 


ci -o r^ 


u 


Z 


** 




a 


• • 


• 


• 


• 


• 


• 


1 


• 


# 


• 


• 


• 


• • 


o 


3 


X 






O 00 


0- 


00 


•o 


m 


ro 


00 


in 


CM 


>* 


Cl 


(SI 


-t O 


-1 


O 


< 






•-« 








—i 


H 
















UI 


CC 


3L 


to 
to 


• 
o 




























> 
1 


o 
I 

CM 




< 


z 


•"* CM 


CI 


4- ITl 


rM 


CM CI 


«* 


m 


■* 


CM Cl 


UJ 


UJ 




X 






























to 
u 


to 

•X 

o 



• UI 

o o 



OC < 

U- OC 



112 



CD 



C\J 

CO 

CD 

-Q 

CO 



o 




Q. 




E 




O 




o 




00 




1 




•t | 




o o 


<d- 


• 


en 




•— 


ii 


«r* 


co 


CD 


00. 


--*. 




03 




3 


• 


O" 


c 


x: 


o 


+-> 


• r— 


s- 


4-> 


03 


-3 


LxJ 


i — 




o 


O 1/ 


S- 




+-> 


e 


E 


o 


O) 


•1 — 


C_) 


+-> 




ra 


r— 


s- 


LU 


CT> 




<L) 


o 


+-> 


4-> 


E 




i—i 


_l 




^r 


+-> 




O 


E 


<d 


0) 


s_ 


+-> 


ff— 


to 


Q 


>> 




00 




4- 




O 




0) 




V) 




c 




o 




Q. 




in 




CD 




a. 









o 




•M 


•c 


ir r- 


o- 


r- 


r- -o 


«N4 


in 


a 


CiriH 










M-4 






•» 


OD --> 


■o 


C 


a- r- 


-Ml 


tr 


40 


40 


r>j 


f-4 f—l -4 










-1 O 


111 


* 


o r» 


to 


fO 


ri i-t 


•— » 


o © 


o o o o o 










3 


•— ' 


to 


N 


—1 o 


O 


o 


o o o 


o 


o 


o o 


o o o 










< 


K 


< 


o o o o o 


o o o 


o 


o 


o o o o o 










a 


< 


o 


• 


• • 


• 


■ 


• • 


• 


• 


• 


• 


i 


• • • 










I o 




o o o o c 


o © o 


o 


o 


o 


o 


o o o 












































z 






























to 




(X 


f— 


mm| 


M* 


o- a 


m 


m 


00 O 


tf\ 


o- 


tn 


r- 


r- 


■4- r- r- 






LU 




< 


a. 




<c 


in •£> 


tr 


o 


o -*■ 


og 


r- 


rg 


00 


rg 


oo 40 -g- 






f— 




LU X 


UJ 


(M 


tn ro 


eg 


rg 


r- ro 


rg 


PMI 


•-4 


rg 


f-4 


o o o 






1- 




z 


•a 


lO 


f-4 


O O O O 


O O 


O O 


o 


O O 


o © o 






Ct 




— 


a 


< 


o o o 


o 


O 


O O O 


o o 


O O O O O 






UJ 




_J 




u 


• 


• • 


• 


• 


• • 


• 


• 


• 


• 


• 


• • • 






O. 










o o 


o o o 


o o 






O 




































or: 




































a 












































t — * 


o 


(M C 


rg m 


in v» f- 


f— . 


f- 


>*■ 


f-< 


0» 83h 






-i 








O oo 


1-4 


4<t-t o 


O O <r\ ro 


o 


in 


CD 


O- 40 -4 






< 








lu a. 


e 


o >0 


rg 


r» 


r- r- 


ro 


(\J 


rg 


■Ml 


in 


If 45 f-4 






Q 








a o 


*• 


a- to r- 


■* 


4- in 


«* 


40 


rg 


O oo f\i m m 






O 








U- — 


o 


O —i 


t— i 


rg 


rg in. 


oo o m 


m 


ro 


f-4 .»• rg 






X 










• 


• • 


t 


t 


• • 


• 


• 


• 


• 


• 


• • • 


UJ 














o o o o o 


o o o 


r-t 


t-H 


M4 


ro 


u- go a 


o 

a. 
O 






































































LL- 












UJ • 




































a o 
























CS 












o Z 


f-4 


»v m 


•* 


in 


— rg 


f. 


<» 


in 


r- 1 


rg 


ro •>* m 


< 












X 
























o 

LU 












o 
























I 












•* 
























»- 












"v ec 


ro 


f» 00 


m 


fO 


m r- 


*-* 


MM| 


<r> 


OO 


rg 


in rg & 














«M Q 


in 


->* t-4 


00 © 


CT f> rg 


O 00 


rg 


^t 


ro O 43 


UJ 














-i- rg ,* 


•H 


o 


rg «*■ 


-* 


O rg 


40 


O 


oo rg oo 


IM 












UJ _l 


r- 


*- 00 


o 


© 


O- rg 


(M 


m 


40 


a 


a- 


oo © o> 


M— 












to < 


a 


a o 


a 


o 


O O 


O 


o 


o 


o o 


a 












< 3 


• 


• • 


# 


• 


• • 


• 


• 


• 








< 












CJ 1- 


o 


o o 


o 


9-* 


— i —t 


M-^ 


w~* 


MM1 


f-4 


f-H 


f-4 m4 f-4 


a! 












o 
























Z 












«J 
























-J 




LL 








o 
























o 




o 








•v < 


t-4 


«* ro 


ro 


oc 


•C •* r- 


f-l 


rg 


<»■ 


ro 


45 <f- f-4 


y- 






on 






<-» a. 


fO 


>o •»>• 


•* 


•H 


r-i a> 


vO 


o 


ro 


m 


CO 


43 00 r- 






z 


z 






a 


CO 


O 00 


•0 


o 


»t CO 


r- 


ro 


O 


OD 


>t 


rg C* CJ* 


Q 




o 


o 






UJ 


o> 


•-" r-t 


o- 


c 


O O 


O 


O 


MM] 


O O O O O 


UJ 




oo 


M- 






co -j 


Cr 


o o 


cr 


o 


O O 


O 


o o 


o © o o o 


CO 




— ■ 


t- 






< < 


• 


• • 


• 


• 


• • 


t 


t 


• 


• 


• 


• • • 


3 




a 


3 






CJ 3 


o 


t-< t-) 


o 


•—< 


•—> r-l 


f-t 


r- 1 


f-4 


f-4 


f-4 


MM f-l 1-4 






< 


_1 






►- 
























CO 




a. 


o 






cj 
























•— i 




X 


00 






< 




























o 
































MM. 




o 








>. 
























X 












O 


«r 


<o tn 


m 


as 


^ o- 


o- 


40 


40 


ro 


m 


ro >» O 


LU 












< o 


to 


rvj ^ 


•g- 


o 


O m 


a 


— 


>t 


f-4 


ro 


cr <*■ o- 


-1 












0- < 


tO 


^ -c 


<Ti 


o 


<\J o 


(E 


40 


O 


cr- 


-r 


ro ro 45 


03 


cu 










O at 


r» 


«»■ «!■ 


cr 


o 


ro o 


m 


o 


a- 


oc 


cr 


cr oo oo 


O 


CJ 










a 


a> 


tr a 


a- 


o 


oo cr 


it 


o- 


00 


00 


X 


on od oo 


at 


a 










_i 


• 


• • 


• 


• 


• • 


• 


• 


• 


• 


• 


• • • 


a. 


O 










< o 


o 


o o 


o 


f-4 


o o 


o 


o 


© 


O 


o o 




LL 










3 Z 
























o 












h- 
























< 


e 










O 
























ec 


< 










< 
























D 

-J 

< 


or 
o 

LU 












rO 


-t tn 


r-> 


r- 


«» %0 


PO 


40 


© 


m 


f— t 


r- oo f-4 


3 


X 










<M 


m 


.* •«■ 


>r 


00 


m so 


•c 


•-4 


ro 


rg 


ro 


4" -4 00 


D- 


t- 


z 










r- 


cr od 


r- 


00 


00 •— < 


r- 


OD 


4T 


r»- 


00 


r- m- 4- 


O 




LU 








UJ 


-* 


in © 


•* 


>!• 


<!• oo 


r> 


■* 


r- 


M4 


CO 


»»■ rg r- 


< 


LU 


UJ 








13 to 


<o 


#-« o* 


-* 


«-i 


in rg 


rg 


o 


45 


r- 


in 


45 •*■ in 




KJ 


3. 








< <t 


• 


• • 


• 


• 


• t 


• 


• 


• 


• 


» 


• • • 


z 


— 


t- 








a. cj 


eg rg Cr oo r- 


r- if. 


rg 


o- 


in 


40 


in 


s* ro «-4 


f— 1 


or 


LU 








O 


mm) 


r-J 






•-4 «H 


*-» 














< 


<E 


^ 






a. 
























a 

UJ 


LU 

z 


1- 


CO 






< 


m4 


o r- 


r-* 


tH 


<7> ^> 


r- 


40 


rg 


<r 


oo 


m r- ao 


1- 


•— « 


ȣ, 


LU 






LU m- 


* 


m rg 


<0 


V 


ro <» 


r-i 


I— * 


45 


n 


4J 


m f-4 rg 


3 


— 1 


LU 


I 






z 


IT 


© m 


<o o^ 


•O •-! 


tT 


ro 


ro 


00 


a- 


mh m r- 


a. 




X 


u 






<-. UJ 


<-\, >j- m 


00 


■* 


rg m 


r- 


>» 


a> 


i^- 


>» 


oo ro ^ 


X 


o 


LU 


z 






-J to 


C«IM^ 


P4 


--I O 


o 


40 


ro 


m4 


f— i 


IMH^ 


o 


►- 


CJ 


•— 






< 


• 


• t 


• 


• 


• • 


• 


• 


t 


• 


• 


• • • 


CJ 




< 


MM 






U 


eg 


rg o 


oo 


r- 


«3 m 


rg 


0D 


m 


40 


in 


«»■ ro m-1 


w 


a 


-1 










-h 


•H r-< 






^- -H 


■H 














LU 


a. 


o 






























to 


CO 


00 


z 






























co 


_> 


tart 


3 








fM 


r- eg 


^-< 


m 


^ ro 


O 


00 


>t 


a 


© 


oo r- m 


< 




o 


u 






-I 


P 


«» f- o 


•o 


>1- o 


>*• 


--4 


in 


rg 


0- 


--> * ro 


X 


to 




a: 






< o 


r- r~ 


r- 


00 


<C OD 


r- 


r- 


oo 


r- 


•«■ © <r ro 




•MM 


LU 


o 






13 «tt 


■* 


o o 


•-4 


«r 


m i-i 


co 


•-* 


ro 


rg 


rg 


r- o m 


X 




> 








t~ a. 


CJ> 


in o 


m 


mH 


o a 


cr 


40 


ro 


t-> 


f-4 


Nm4< 


u 


>- 


r- 


z 






« 


CM 


rg o 


ao 


r- 


« <»■ 


i-i 


OC 


in 


40 


m * ro mi 


UJ 


M 


< 


< 








■Ml 


f-l t-4 






r-l r4 


f— i 














o 


_J 
































u. 


o 


LU 


00 






























o 


-J 


ae 


oo 








* 


r» a 


r- 


•O 


<* ro 


o 


»-M 


00 


<*• 


r- 


in oo m 




UJ 




< 








fO 


00 rg 


m 


o 


rg ro O 


in 


rg 


CO 


rg 


I0OH 


>- 


> 


z 


X 






o 


CL> 


m r- 


o 


00 


r- r\ 


o 


tr 


in 


Pfjl 


o 


45 4- go 


1- 




3 








O «* 


tn o <o 


m 


>*■ 


rj> r"i 


o 


© 


U> 


!> 


ro 


NmImI 


— 


Q 


X 








Z a 


IM 


rg o 


LT 


-H 


rg u\ 


to 


in 


Cr 


00 


r> 


r- m 45 


CJ 


Z 


•— 








a 


• 


• • 


• 


t 


4 • 


• 


t 


t 


t 


• 


• • t 


o 


3 


X 










<*> to o ao 


r- 


a> m 


<M 


o- 


m 


»3 


in 


* ro m. 


-J 


O 


< 










M-4 


—4 — 






f-l »H 


^4 












UJ 


a. 


X 








to • 

CO o 
























1 

f-4 


O 
1 
rg 










< z 


»H 


rg ro 


^l■ 


m 


»i rg 


r-i 


>* 


m 


f-4 


rg 


ro >j- m 


UJ 


UJ 










X 
























CO 

< 

CJ 


co 

< 



• UJ 

a o 
uj z 
oc < 
U. a. 



113 



o 



JO uj 
3— «/> 
■ay- •* 
ac « o 

ac 
> 

1 o 



Z 4 «/> 

»- O < 
-I O 



go m r- a* p» 

gj- cc — ■ ~c a 

♦ OMnn 

o o o o o 

• • • • • 

o o o o o 



mN * m N 

p- oo in o gr 

00 P"> CM «M -* 

o o c o o 

o o o o o 

t • • • • 

o o o o o 



r- oo gj> pg gj 

0*1 •-••■* O O 

o o c o o 

o o o o o 

• • • • • 

o o o o o 



•t •— <f •c cc 
<* gj in po ec 

lf» M p- H O 

o o o o o 
O O o o c 

t • • • • 

O O o o o 



u\ cr er if* «-> 

«(MHrtH 

o o o o o 

o o o o o 

o o o o o 

• • • • • 

o o o o o 



•t co in <o it. 

IT, g} *t P" 1 <M 

— o o o o 

o o o o o 

o o o o o 

• • • • • 

o o o o o 



4 

a 

a 



tu a 

ac o 





c 




CD 




c 




o 




Q. 




E 




O 




o 




oo 

■ 




1 

2: 




«LO 




O O 




"3" • 




cn 




r— n 




•> 




a; ca 




_*: 




fO 




3 • 




a- c 




.c 


co 


+-> •!- 


i — 


s- +-> 


• 


<o 3 


CO 


LU 1— 







<u 


00 


r— 


s- 


-a 


-l-> c 


fO 


c 


h- 


a> 1- 




O 4-> 




fO 




1— s- 




UJ 01 




a; 




+-> 




+-> c 




1— 1 




_l 




"3" 4-> 




O 




E a> 




cu s_ 




+-> -i- 




00 Q 




>> 




oo 



OlMlMMir 

H<tB^O 

o o <o n.i r~ 
gj- o> i*> f- g) 
o o — —• <m 
t • « • • 
00000 



m gj r>- t-i p- 

P- P- pn CO Pg 

gf m gj <o co 

po m 00 o if • 

• • • • t 

o O O •-" -g 



>t .— • cr co *— 

m or o ■£ — 

O 00 po in m 

m 0-1 •-• •* po 

• • • • • 

t-* o~ in g; cr 



a: 
C 



10 

£Z 
O 
■— 
00 

ai 
or: 







LU 


• 








































a 


O 












































z 


*-t 


CM 


rr 


■j 


m 


r-> 


pg 


in 


<t 


in 


pg 


P.' 


pr 


g| 


m 


<r 








*r 



< 
































a 

O 

UJ 

X 








»* 


ec 


>*■ CO 


<— < 


»-j 


00 


a 


<C 


r» 


a 


00 


g3 


IM 


PJ 


t— » 


00 










pg O 


«*» 


00 


0" 


0- 


<t 


ri 


<t 


m 


p- 


go 


pg 


pH 


pg 


•-* 


«_« 


UJ 












««• 


m 


0- 





O 


in 


oc 


05 


r- 


gf 


<f 


-» 


-*• 


O 


cr 


rg 








UJ 


_i 


p» 


<C 


O 


a 





O 


,_* 


f-i 


_ 





O 


O O 


--^ 


O 


H 








00 


4 


a 


O 


0- 


cr 


O 


O 


O 


O 











O 


O 





O 


or 








< 


:_> 


• 


• 


• 


• 


• 


• 


• 


• 


t 


t 


• 


• 


• 


• 


• 


<i 








»~ 














<-- 


M 


•-j 


^H 


^t 


*-4 


t-rf 


.-» 


i-4 


— * 


•-g 


Ul 











































Z 










< 
































_i 




u. 







































c 









^ < 


m 


ac 


ao 


in 





pg 


r- 1 


m p- 


* 


in 


O 


pg p- 


O 


1- 






00 


»g 


ac 


Ki 


m a 


cr 


•-4 


fO 


in 


pg 


■* 


f— 1 


H 


O 


~> 


^* 


P- 






z 


z 




O 


p4 


00 0- 


cr 


O 


pH 


pg 


rg 


w— 1 


PI 


,— ) 


•-< 


w-* 


gi- 


po 













UJ 




O 





Cf 


cr 


O 


O 


t— 1 


p-i 


~* 


O 


O O 





O 


O 


UJ 




00 


M 


t/» 


•J 


O 





cr 


O 


OOOOO 


O 


O 





O 


O 


to 




>— 1 


r- 


4 


< 


• 


• 


• 


• 


• 


• 


• 


t 


• 


• 


t 


■ 


t 


• 


• 


3 




a 


3 


O 


D 


f-4 


r+ 


O 





_^ 


r-( 


•-< 


r 1 


,-1 


*-t 


«— 1 


V* 


*-i 


^4 


r-< 






4 


_J 




K 
































00 




a 


O 




O 
































— 




X 


00 




< 




































O 






































*» 









^ 


































X 








O 




00 


CO 


~* 


^h 


00 


O 


-* 


•t 


r~ 


•-> 


O 


(Si 


m 


ci 


m 


UJ 








< 


O 


•»■ 


r-i 


<M 








in 


vt 


O 


O 


pg 


in 


•Ci 


in 


r- 


cr 


—1 








ac 


< 


m 


h- 


O 





O 


cr 


■c 


-O 


gD 


•-^ 


fi 


ra 


r-i 


m 


<c 


00 


UJ 






O 


ac 


00 


v0 


or 





O 


p- 





•0 


■c 


cr 


cr 


cr 


a 


CO 


cc 


O 











O 


t> 


o> 


V 





O 


cr 


cr 


cr 


CT 


Cr 


0- 


cr 


cr 


Cr 


cr 


ac 


ac 






_j 




t 


• 


• 


t 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


a 


O 






4 O 


O O 





-^ 


*-> 


O 


O 


O 


O 


O 


O 


O 








O 




u. 






D 


z 









































r- 


































< 


e 






O 


































ac 


4 






4 


































O 

_i 
4 


ac 


UJ 










f- 


r~ 





O- 


r- 


m 


O 


cr 


O 


•-* 


,H 


^5 


»-• 


r- 


CM 


3 


X 








«M 


«t 


•0 


~c 


•O 


r- 


in 


pg 


gj 


O 


g) 


cr 


v* 


r- 


m 


gf 


i- 


h- 


z 








m 


HI 


«* 


ro 


—* 


•* 


g3 


O 


«r 


pg 


pg 


r- 





r- 


m 







LU 






UJ 


O 


<M 


rg 


-t 


r-t 


■* 


-J 


m 





00 


O 


CP 


in 


CO 


pg 


4 


UJ 


UJ 




O 


LO 


r- 


in 


r-i 


^4 


O 


p4 


cr 


rr> 


•1 


._-* 


O 


pg 


•c 


CO 


cr 




rg 


JT 




< 


< 


• 


• 


» 


t 


9 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


z 


fc- 


H 




ac 


O 


cr 


CT- 


CD 


co 


•O 


>»■ pg 


O 





fp. 


g> m 


pg 


*-< 


O 


*■« 


Ct 


Ul 




O 














^4 


w-< 


<-* 


















4 


CO 


,_, 


ec 




































UJ 


Ul 

Z 


r- 


to 


4 




«»■ 


O 


>» 


in 


ao 


•c 


in 


m 


r~- 


p-- 


m 


in 


1— t 


00 


^-* 


r- 


M 


z 


UJ 


UJ 


«-l 


>»■ 


ro 


eg 





*-* 


pg 


■0 


in 


<> 


in 


in 


rg 


m 


pg 


gj- 


3 


-t 


LU 


X 


z 




CM 


in 


IT. 


«t 


o> 


r- 


c 


CO 


|T| 


p- 


O 


r~ 


pg 


■0 


CO 


a 




z 


s 


H4 


UJ 


P- 


«» 


eg gf 


O 


00 


r- 


* 


u 


P- 


a 


p- 


>r 


r- 


1-* 


z 


O 


UJ 


J 


«/) 


<7> 


0- 


«M 


*-* 


o> 





0P 


pg *■ 


•-* 


cr 


rg 


>© 


00 


a 





H 


LJ 


»* 




< 


• 


• 


• 


• 


t 


• 


• 


t 


• 


• 


• 


1 


t 


• 


• 







4 


w 







O- 


o- 


OD 


00 


-0 


«» 


Pg 





-O 


pi 


PA 


p^ 


pg 


^h 





■-» 


C 


-J 


















f-4 


»~4 


w-i 


















UJ 


a. 


a 




































co 


i/> 


0-1 Z 




































to 


-) 


|M 


-3 






O O 


co 


*c 


<A 


f\ 


a 


pg 


P- 


O 


gj- 


r- 


•C 


00 


pg 


< 




O O 


J 




O r» 


rr. 


•* 


>» 


r- 


in 


m 


>» 


•O 


o> 


O" 


m 


gf 


O 


X 


1/) 




ac 


4 





<7> 





If 


-r 


CO 


00 


#-< 


gr 


O r>- 


in 


m 


a 


CO 


ir 




1-* 


UJ 





3 


4 


m 


>0 


(\J 


>f 





<o 


•-• 


>r 


09 


g} 


00 


p- 


p-i 





—» 


X 




> 




r- 


ac 


<T 


CD 


fM 


r-i 


o> 





r- 


»— » 


m 


w-i 


Cr 


pg 


•o 


CO 


Q- 


u 


> 


*-• 


(_i 


»-> 


CJ 


• 


• 


• 


■ 


fl 


t 


• 


• 


• 


9 


t 


• 


t 


• 


t 


4 


r- 


t- 


z 


< 




IT 


cr 


CO 


UJ 


•0 


gr 


pg 





•O p^ 


pn 


CI 


pg 


«-g 


O 


UJ 


r- 


4 


< 
















<-« 


f-H 


»-• 


















O 


-1 






































UL 


O 


UJ 


00 




































O 


-1 


tc 


</> 






Na)Nom 


00 


P* 





O 00 


g> 


O 


in 


gp 


pg 




UJ 




4 






r\ 


«»4 


<f 


•r 


a 


r* 


O 


a 


•O 


£ 





O 


r» 


if 


■^ 


> 


> 


X 


X 




O 


<o 


rr\ 


^< 


•* r~ 


f\ 


P-^ 





<* 


pg 


m 


NO 


m 


p- 


t- 




Z3 




O 


< 


«vj 


cr 


•* 





<e 


in 





O 


cr 


«H| 


cr 


in 


Cr 


pg 


M 


O 


Z 




Z ac 


*•* 


—* 


m 


•-* 


a 


fp. 


•-4 


IT 


gs 


•—1 


O 


pg 


•0 


CO 


Cr 


8 


z 


ta- 






O 


• 


t 


• 


• 


• 


• 


• 


• 


# 


• 


• 


• 


t 


• 


• 


3 


X 








O O 00 


OD 


<£ 


g)- 


m 





■c 


c\ 


gj- 


ro 


rg 


— 1 


O 


-j 


O 


< 








t-i 


p4 








■H 


•m 


—< 
















UJ 


a 


X 




to 
l/l 


• 
O 
































> 
1 

•— * 


O 
pg 






< 


Z 


■■* 


<M fl 


p4 


pg p-i 


M 


rg 


ro 


g* 


m 


UJ 


UJ 






X 


































4 
O 


i/) 

4 







• 


UJ 








































O O 








































UJ Z 


p^ 










pg 










W 


















ac 


< 








































u. 


ac 





































114 



Q. 

O 

at 
a 



Q 

O 



O (M 

p-< 

_J O UJ 

O ►» «/) 

« r- < 

a < o 

O a 

>» 

X o 
z 

a •— ~* 

< a 

U1I Uj 

Z < to 

•- C < 
_i O 



t — . 
O oo 

uj a. 

cc l_> 





+-> 




c 




a; 




c 




o 




Q. 




E 




O 




O 




to 

I 




1 




*■" c— 




o o 




^t- • 




CTi 




1— II 




« 




a> oa 




j*. 




fO 




ZJ • 




a- e 




.e o 


*3- 


-t-> T- 




S- 4-> 


• 


tO 3 


CO 


UJ i — 




o 


<D 


o oo 


r— 


s- . 


-0 


+-> E 


(O 


e o 


1— 


a> -r- 




o +J 




co 




i— s- 




UJ O* 




a> 




o +-> 




+-> E 




1— 1 




s: 




^ 4-> 




O 




E <V 




Q) i- 




+-> -r- 




co Q 




>. 




OO 



0* h- CO co o* 

ao —. «r ,-■ r- 

>»■ 1NJ rf —• O 

o o o o o 

t • • • • 

o o o o o 



>0 s r-- on 0* 

r- o «© cm -o 

cm O ~C m en 

cm •-• o o o 
o o o o o 

• • • • • 

o o o o o 



O CM 0" CM Ifi 

ri 4 00 >]- o 

o o * cm r- 

^ 9> it\ r^ >t 

O O -. -I CM 

t t • • t 

o o o o o 



4 eg co ir. c- 

o- m co or cm 

r»- CO CM fl t-1 

C O O O o 

o o o o o 

• • • • • 

o o o o o 



•O O' >t> co f~ 

ft ci in op c* 

CM m CO CM •— 

•-• o o o o 

o o o o o 

• • • • • 

O O o o o 



m -a r- .-. r» 

© o co <o o 

r- r- c > cm cm 

«* m -4- >© cm 

CM \f\ ao © UN 

• t • • • 

O O O -< ~- 



t-t CO 00 O f 

co m m co cm 
•-< o o o o 

O O O O o 

o o o o o 

• • • • • 

o o o o o 



axte 40 

>C vO O 00 >c 

CO <-* «-< o o 
o o o o o 
o o o o o 

t • • • • 

o o o o o 



*t —4 <*• (D f* 

hit in«H 
O « cm m in 
m co -h -4- cm 

• • • • • 

^ w ^ Off 



o 
cc 

o 
u. 



<D 
to 

E 

o 
a. 

a; 

OC 





Q O 


























o 






O Z 


w* 


CJ 


tr\ ^ 


in 


•-I 


<M 


m 


<t 


m 


•-* 


CN' CO 


.*• m 


•or 






X 


























ac 

Q 

UJ 






o 


























X 






< 


























r- 






■v 0C 


<r\ 


IA 


m >o 


<£ 


CO 


■* 


>0 in 


m 


ON 


4 >0 


CO v0 








(VJ O 


if\ 


l>- 


(M & 


m 


o o 


CJ> 


INJ 


o 


CO 


a cm 


r- o- 


UJ 








o r- 


tr\ f\i o 


*>4 


^4 


o 


O 


o 


CO 


m on 


ON >o 


rsj 






UJ _> 


IA 


(M 


»» a 


O 


>»• 


(M 


CM 


in 


00 


O 0" CO 


o o 


*— 






i^ < 


<y 


a 


a a- 


O 


o 


O 


o o 


o 


vH 


o o 


•— • •—» 


a. 






«* 3 


• 


• 


• • 


• 


• 


• 


t 


• 


t 


• 


• # 


• t 


<t 






o ►- 


o 


o 


o o 


•-< 


rH 


*~t 


»— 1 


•-< 


f-4 


tmt 


»-4 pH 


f- •*! 


UJ 






o 


























z 






< 


























_J 




u. 


13 


























o 




o 


■^ < 


•*• 


a- 


O ao 


CM 


o 


00 


in 


CM 


r- 


r- 


r^ in 


CO ON 


K 




oo 


<-• 0L 


<x> 


•c 


rg m 


— < 


«*• 


m 


IN 


O 


•^ 


co 


o *- 


<f ac 






z z 


Q 


rH 


i- 


r*i t*i 


O 


CM 


m 


CM 


r- 


O 


O 


in co 


CM CM 


C 




o c 


UJ 


O 


o 


^ O 


o 


c o 


O 


cr- 


CM 


p^ 


O O 


p-l »H 


UJ 




00 — . 


l/> _J 


o o o o o 


o> 


O 


O 


a 


o 


o o o o o 


oo 




«- K 


< «» 


• 


i 


• • 


• 


• 


• 


• 


• 


t 


• 


• • 


• • 


-> 




a ^ 


l_> 3 


f-i 


|M 


•^ r< 


f-t 


o 


t— * 


— i 


o 


p-4 


fH 


«-l pH 


•I .-1 






< _i 


►- 


























oo 




0l o 


O 


























»— 1 




x oo 


< 






























o 




























■PM 




o 


«v 


























T 






o 


as 


m 


in r^ 


1^ 


oc 


0~ 


INI 


CM O 


m 


ON CM 


r- -t 


UJ 






< o 


o 


-c 


«t <c 


a> 


o 


a 


>t 


<0 


a> 


* 


h r- 


«t H 


_J 






a: < 


c»l 


oc 


m h- 


o- 


00 


r- 


m 


CM CT 


-4 


CO O- 


vt CO 


CO 


UJ 




C a 


ir> 


•— i 


(\l oc 


o> 


0> 


-t 


^ 


<0 


CNI 


<o 


o -O 


in in 


c 


l_) 




O 


o> 


o- 


o- cr 


a 


r- 


a 


O- 


oo 


00 


00 


00 00 


ao ac 


ac 


ac 




—i 


• 


• 


• t 


• 


• 


« 


• 


• 


• 


t 


t t 


t • 


a 


O 




< c 


o 


o 


o o 


o 


o 


o 


O 


O O 


o 


o o 


o o 




u. 




3 z 


























o 






K 


























«j 


is 




u 


























ac 


< 




< 


























O 


OC 

o 

UJ 






o 


IT 


-*■ o 


.*■ 


w-t 


CO 


m 


•J- 


CO 


o 


on r» 


CM IN 1 


3 


I 




fNJ 


r-* 


v~i 


m ao 


•4" 


•a 


CM 


>» 


m 


CO 


CO, 


CM CO 


Ci CM 


K 


*- 


z 




•-4 


f*l 


m m 


o 


CM 


IP 


in 


in 


■t 


O 


cm in 


cm in 


o 




UJ 


UJ 


tH 


IT 


■n o 


in 


fi 


m 


w; 


f-l 


r- 


m 


in cm 


CO CO 


< 


UJ 


111 


O »/) 


o 


(SJ 


<\J CO 


•-4 


o o 


>o 


co 


in 


j- m 


co m 




fsJ 


X 


< < 


• 


• 


• • 


• 


t 


• 


• 


• 


• 


• 


• t 


• • 


z 


»-t 


r- 


a o 


«M 


•-- 


c 00 


r- 


<0 


ITi 


CM 


ao 


in 


<0 


m ■»■ 


CO ft 


— . 


or 


Ul 


a 


—4 


^^ 






•-* 


^^ 


—I 














<f 


CD 




























c 


UJ 


mm 


ac 


























UJ 


z 


r- CO 


< 


(TV 


««■ f- 


CM 


<a 


ro 


ac 


oc 


o 


CM O 


O f- 


»- 


•— 


*C UJ 


UJ f-l 


* 


r~ 


O m r- 


* 


PH 


CO 


m 


* 


04 


CM <o 


O r~ 


3 


—1 


uj X 


z 


a 


fS) 


<m m 


CO 


m 


oo 


-* 


r\ 


<c 


CO 


co r- 


o -» 


a. 




x o 


•— UJ 


in 


(Ni 


m m 


•»■ 


CO 


r- 


>1 


ao 


r- 


iT 


O -o 


«* o 


X 


o 


UJ Z 


-I CO 


<o f\J 


o> ^ > 


.-i 


CM 


r^ 


au 


•-I 


o 


ON 


O 0* 


o <» 


o 


r- 


o •- 


< 


• 


t 


• • 


• 


• 


« 


• 


« 


• 


• 


• • 


• • 


o 




4 — 


U 


(M 


(NJ 


cy oo 


r^ 


in 


-t 


#-i 


oo 


m 


m 


m >»■ 


CO i-l 


«^ 


O 


_) 




^4 


•— » 






vH 


»-H 


t-* 














UJ 


a. o 




























oo 


to 


to Z 




























oo 


_J 


►- 3 




o> 


•-« 


—i m 


m 


ac 


«!■ O 


m 


CO 


C •* 


CO CO 


< 




u u 


-J 


•H 


*> 


o — 


ao 


r- 


-»• 


co 


«~l 


o 


m 


On u , 


.0 ao 


X 


to 


a 


< o 


W3 0" ro m f- 


u 


in 


r- 


c. 


<o 


•0 


^ -r 


CM <C 




— . 


UJ o 


3 «f 


m 


(NI 


CM CM 


•♦ 


o 


INJ 


*-* 


o 


r- 


co r- m 


O CD 


X 




> 


i- ac 


<o 


^J 


09 -1- 


w— 


-*■ r^ «o 


INI 


V 


o> 


ON ~> 


O CO 


u 


> 


— (J 


CJ u 


• 


t 


• • 


• 


• 


t 


9 


t 


t 


• 


t • 


t • 


•* 


r- 


t- z 


« 


rsi cm cr oo r- 


m «»■ 


•-I 


ao 


* 


m 


•4 •*■ 


CO i-i 


UJ 


«- 


< < 




•H 


^H 






■H 


#-t 


•-» 














O 


_J 




























U. 


o 


UJ IS) 




























O 


-1 


ac uo 




* t» 


C» r>- 


W3 


tt CO 


PH 


oc 


j;r-ificoin 




UJ 


< 




fO 


00 


CM 1*1 


O 


CM 


•n 


© 


m 


CM 


CO 


CM 00 


O ft 


>- 


> 


z z 


o 


00 


m 


r~ o 


0D 


r- 


co o O in 


ft 


O -O 


<t o 


»- 




3 


O < 


m 


o 


c»i r^ 


-t 


cy 


c> 


o 


O ON 


0> 


co r» 


ft ft 


p«i 


a 


X 


Z ac 


CM 


(M 


-o m 


w* 


CM 


m 


m 


m 


a 


oc 


r- r- 


m ~o 


o 


z 


•— 


o 


• 


t 


• • 


• 


• 


• 


• 


t 


# 


• 


• • 


• • 


o 


3 


X 




«n 


m o oo t- 


G* 


m 


IM 


o- 


m 


sO 


m >t CO rH 


_i 


O 


< 




tH 


»H 


•-i 




H 


•— * 


•-* 












UJ 


ac 


X 


to • 

to o 


























> 
1 

•-I 


o 
i 

CM 




< z 


f-4 


«M tri 


■H 


CM 


rr\ 


-l 


in 


H 


CM CO 


•4- m 


UJ 


UJ 




X 


























00 

< 


to 

< 
l_> 



o o 

UJ Z 

ac < 
u. or 



115 





C 




Q) 




C 




o 




Ql 




E 




o 




(_> 




on 

■ 




1 




■ LO 




o o 




•3- • 




CT> 




r— II 




■ to 




CD CQ 




.*: 




CO 




3 • 




O" c 




-c o 


LT> 


+-> •■- 


r— 


s- +-> 


• 


CO =5 


CO 


UJ i — 




o 


<D 


o to 


r— 


S- 


-Q 


+-> E 


rO 


C O 


c- 


CD 1- 




C_) -t-J 




<o 




i— s- 




UJ CTi 




CD 




O +-> 




■M C 




i— i 




s: 




^- -m 




o 




E CD 




O) S- 




•4-> -i- 




CO Q 




>> 




CO 




4- 




O 




CD 




to 




C 




o 




Q. 




to 




cd 




q: 





u 




«\J 


NOnO-f 


♦ cm co m cr 


HAD CD O^ 






« 






^ ^ (O (fl O 1 


» KM" Ot) N 


co m co c«> cm 






_> o 




UJ 


»« + -<f- 


h- CO «NJ —i t«« 


-* O Q O O 

o o o © o 






3 — 




(/) 


.* IM _i ^ O 


O O o o o 






< 1- 




« 


o o o o o 


o o o o o 


o o o o o 






a < 




<_> 


• • • t • 


• • • • • 


• • • • • 






o or 

>v 
z o 

z 






o o o o o 


o © o o o 


o o o o o 


















i/> 


or »- 




IN 


•— • — • cr a *-• 


cninir^ 


or. k «» ~* in 




UJ 


<t a. 






r- -t «o od i*- 


CO f- * o CO 


h ^ o it r. 




»-• 


UJ X 




UJ 


* r- >«• co cm 


(DmMHpt 


cm o o o o 




t- 


z < 




«/> 


— o o o o 


o o o o o 


o o o o o 




(X 


•- 3 




4 


o o o o o 


o o o o o 


o o o o o 




UJ 


-j 




u 


• • • • • 


• • • • t 


• • • • • 




a 
o 
a: 

a 








o o o o o 


o o o o o 


o o o o o 






• 


„. 


O CM 0* CM f> 


U\ -O 1- »h f- 


^ «-l CT 00 W— 




-j 




O CO 


—> ~t 00 -4" O 


O O «*> co O 


IT CO 0> 4 ■-■ 




< 




UJ 


a 


O O <C CM 1"- 


f- r>- CO CM CM 


fHiAir 4h 




a 




or 


U 


* cr co r- •* 


4-lfi -» ON 


o oo n if in 




o 




u. 




O O — • r~> <M 


CM m 00 O ft 


Ifl CO «-l «jr CM 




X 








• • • • t 


• t • • t 


• • • t • 


UJ 










o o o o o 


o o o •-> — ■ 


—i co m * cr 


o 
o 





o o 
























o 






o 


z 


p-< i\l ro >t 


m 


— * CM 


pr 


^~ 


m 


f— 1 


Ol 


ro 


^1- 


in 


< 






X 


o 

< 
























or 

o 

UJ 

I 






^. 


or 


00 cm (»■> O 


CM 


cr oo 


-* 


o 


•— < 


o 


CD 


ec 


0D 


a 








CM 


o 


CO f\ (•- 00 


CO 


in r^ 


^-< 


o- 


m 


O 


CD 


O 


~0 


00 


UJ 










CM «*> C7> 0> 


o 


cj> ro 


-* 


<f 


•4- 


«jr 


CO 


J- 


o 


o> 


OJ 






UJ 


-j 


m cm o <y 


o 


0> ^4 


*_• 


!H 


O 


o 


O O 


t— t 


o 


•-* 






l/> 


< 


o* o o &• 


o 


Cj- o 


o 


o 


o 


o 


O O O 


o 


or 






< 3 


• • • • 


t 


t • 


• 


f 


• 


t 


t 


• 


• 


• 


< 






O 


o 

< 


o o o o 


t-* 


o -« 


•-* 


*-* 


1— * 


tH 


»-i 


•-( 






UJ 

z 
_J 




U. 




o 
























o 




o 


v. 


< 


00 O 0> O" 


in 


O co 


m 


ro 


in 


<# 


»H 


CM 


ro 


cr 


►- 




l/l 


w t 


QC 


•-- 


00 o 


r<"v 


O 


o 


a 


CO o 


ao 


«* 






z z 




Q 


JJ O f/ ^ 


o 


00 CM 


CM 


CO 


«* 


o o 


•-« 


~f 


-»■ 


o 




o o 


UJ 




o o o> o 


o 


o- ~ 


f-« 


,— i 


o 


o o o o o 


UJ 




00 — 


</) 


-J 


o o o o> o 


a- o 


o 


O 


o 


o 


o o o o 


to 




«-»- 


< 


< 


• • • • 


• 


• • 


• 


• 


• 


• 


• 


• 


• 


• 


3 




et 3 


U 


3 


— — o o 


~-4 


O -4 


^H 


^H 


w~* 


•— l 


pa< 


■-« 


w-i 


H 






< _i 




t- 
























to 




a. o 




O 
























i— < 




X to 




< 




























o 




























»n 




u 


«v 


























X 






o 




^ f*> ^" *-« 


~t 


CO -o 


0^ 


nO 


CO 


o 


0^ 


(\J 


PM 


CO 


UJ 






< 


o 


•C Ifl CM O 


CM 


r- ■£> 


CI 


s0 


CM 


in 


in 


^r 


cr 


CO 


_J 






or 


< 


<# 0D O O 


O 


■o in 


-4" 


r\j 


r- 


w~* 


f-H 


r-4 


O 


CM 


CQ 


UJ 




Q 


or 


>o ■*• 00 o 


o 


t>- m 


in 


m 


00 


<r 


cr 


cr 


er 


CO 


O 


o 






o 


o^ &■ c> o 


o 


a- o* 


a 


o> 


cr 


o- 


cr 


a 


rr 


cr 


or 


or 




_/ 




• t 1 • 


t 


• • 


• 


• 


• 


• 


• 


• 


• 


* 


a 


o 




< 


o 


O O o ^ 


t-4 


o o o 


o 


O O 


o 


o 




LL 




3 Z 
























e> 






»- 


























< 


o 




U 


























or 


< 




< 


























a 

< 


CC 

o 

UJ 








CO ^ 00 •-* 


rH 


or r» 


(O 


o 


in 


CO 


r~ 


o 


■j- 


>» 


3 


X 






CM 


CM w-t CO 00 


CO 


CM -H 


f^ 


vO 


CM 


CO 


O'- 


r- 


r\i 


r- 


r- 


t- 


z 






CO f- CO CM 


in 


CO CO 


PO 


in 


a 


CO 


er 


>»• 


a 


o 


u 




UJ 




UJ 


ONN't 


•— 


CM •♦ 


o 


on 


•o 


» 


r- 


-«■ r- 


■— • 


< 


UJ 


ID 


O to 


CO O CM r- 1 


o 


o r- 


P-H 


PO 


i— » 


cr 


(NJ 


o 


oo 


cr 




INI 


X 


< 


4 


• • t • 


• 


• • 


• 


i 


• 


t 


• 


• 


• 


# 


z 


fc- 


I- 


ac o 


on oo ao oo 


<£ 


>*• CM O 


<o 


CO 


CO 


ro 


CM 


«-i 


o 


M 


or 


Ul 


O 








— » •— < 


•-4 


















<r 


00 




























o 


UJ 


mm 


or 


























UJ 


z 


t- 00 


< 




hhO<0 


<<• 


00 il 


cr 


o 


•— 1 


f- 


>»• 


■* 


>o 


CM 


»- 


M 


4. UJ 


UJ 


-* 


h400» 


<o 


•— < ^-1 


in 


o 


ao 


•0 


cr 


>o 


ro 


00 


3 


_l 


UJ 1 


z 




in -o if* co 


o 


CM «-l 


m 


ro 


r^ 


m4 


o- 


o 


CO 


4 


a 




X o 


•^ 


UJ 


CO CM CM <»• 


^4 


«-l CM 


•♦ r- 


<c 


00 


•G 


CO 


«0 


p-4 


X 


o 


UJ Z 


_i 


(/> 


cd r- rg _, 


a> 


O f- 


•M 


CO 


1— t 


cr 


CM 


^0 


oo cr 


o 


f- 


o — 




< 


t t • i 


• 


• • 


• 


• 


• 


• 


• 


• 


• 


1 


u 




< ~ 




U 


O o^ oo ao 


•c 


.»• CM 


o 


>o 


CO 


CO 


ro 


CM 


•-> 


O 




o 


_l 










w+ *~t 


— < 


















UJ 


a o 




























to 


to 


oo z 




























to 


3 


— 3 






tr\ CO O !•» 


CM 


<r m 


cr 


ro 


<«• 


CM 


cc 


•c 


p- 


<* 


< 




O (J 


-j 




*^«4 


>o 


0- fj. 


cr 


cr 


O 


cr 


CM 


cr cr. 


r«- 


X 


oo 


or 


< 


o 


cd ao in -r 


V 


co tr 


•-t 


#— * 


in 


r- 


P» 


co 


a 


o 




*■* 


UJ o 


3 


< 


4-orvj^ 


o 


CM 43 


CM 


a> 


m 


r- 


O 


ro 


m 


*M 


X 




> 


1- 


or 


r- vO ini -■ 


0> 


O in 


O 


CM 


»H 


er 


CM 


*j 


CO 


cr 


u 


> 


— CJ 


U 


u 


• • • • 


t 


• • 


t 


• 


t 


t 


• 


• 


• 


• 


1 


r- 


t- z 


« 




0* O CO CO 


<o 


■*• CM 


O 


-o 


CO 


CO 


ro 


OJ 


r-t 


o 


UJ 


M 


« < 










-* •-« 


•-* 


















U 


-J 




























u. 


o 


UJ 00 




























o 


-1 


at oo 






CM 00 CM O 


CO 


oo r- 


o 


o 


00 


*»■ 


O 


iri 


•t CM 




UJ 


< 






CO — *■ >t 


<J> 


«-• o 


a- 


o 


<o 


o 


O r- 


m 


»-* 


> 


> 


X X 




o 


4)I<1H^ 


r- 


CO CO 


o 


-t 


in 


CM 


m 


-o 


m 


r- 


t- 




3 


o < 


MtM>-t 


o 


•O in 


c 


o 


<7> 


p4 


cr 


in 


0» 


CM 


tart 


c 


X 


Z 


or 


i_l _■ CO ■-■ 


cr 


CO -H 


m 


-0 


~* 


o 


cm <o 


ao cr 


«J 


z 


»* 




o 


• • • • 


• 


• • 


• 


• 


• 


• 


• 


• 


• 


• 


D 


3 


X 






O O CO CD 


-o 


»»• CO 


o 


sC 


CO 


•<■ 


ro 


CM -H 


o 


_) 


o 


< 






.-» -H 




<— t *-H 


t— . 
















UJ 


a 


X 




























> 


o 



O0 • 

oo O 
< Z 



• UJ 

a o 

UJ z 

or «x 
u. or 



•-• cm co ^- m 



HNCn^m 



•i cm co ^ m 



oo 

< 



116 



>t cr >o *r> oo 
co i^ -#o h" oo 





+j 




c 




a> 




c 




o 




Q. 




E 




o 




c_> 




oo 




1 




+> r— 




o o 




^f- • 




CTi 




■— II 




« 




ai ca 




^ 




ra 




3 • 




O" c 




-c o 


CO 


+J •!- 


i — 


S- -t-> 


• 


fO 3 


00 


LU i— 




O 


CD 


O OO 


r— 


S- 


-Q 


+-> c 


<a 


c: o 


J— 


a> •■- 




CJ> +-> 




(O 




i— t_ 




uj ai 




cu 




o +-> 




+-> c 




t-H 




31 




«3" +-> 




O 




E CD 




a> j- 




4-> •■- 




CO Q 




>> 




oo 





-j 


o 




UJ 


r- CO OD Co m 




3 


•— ■ 




to 


o of «\j co .-i 




< 


t- 




< 


o o o o o 




a 


< 




o 


• • • • • 




o 


a 






o o o o o 




> 












I 


O 

z 








oo 


a 


9— 




•-4 


r- o> m < in oo 


UJ 


« 


a 






co h^ of or oo 


■— 


UJ 


a: 




UJ 


CM 0C CM (7- •£) 


o- 


z 


«i 




OO 


>» t-" -^ o o 


a 


— 


c 




< 


O O O O O 


UJ 


-J 






cj 


t • • • • 


a 










o o o o o 


O 












CC 












a 


















• 


—» 


O CM O* CO UO 


-j 






o oo 


H4- to <t O 


< 






UJ 


0. 


o o -o co r- 


a 






ex 


o 


«*• 0» c\ r- oj 


o 






u_ 


«- 


OOhhn 


i 










• • • • • 



oo of m o- oc 

<r c -o -o u" 

m f- of co co 

•-< O O O O 

O O O O O 

t • t • • 

o o o o o 



co of c- m o 

r» 03 fi O m 

r-t C 43 U0 fO 

CO O O O O 

O O O O O 

• t • • • 

o o o o o 



—. 03 r- •-« eg 

co —. O O o 

o o o o o 

O O o o o 

• • t • • 

o o o o o 



IT 9— CO CO 03 

03 CO «o *-• t-l 

O O o o o 

o o c o o 

• • • • • 

o o o o o 



o o 

a z 

a: 





i/i < 




< 3 




CJ *- 




CJ 




< 


u. 


o 


O 


>s < 


oo 


— a 


z z 


o 


o o 


UJ 


00 <— 


oo _i 


■- K- 


< < 


or. 3 


<_) 3 


4 -1 


»- 


a. o 


<_) 


Z oo 


< 


o 




<-> 


v. 



< o 

3 Z 



< 



a> 
</i 

sz 
o 

Q- 
(71 

cu 



UJ 


C3 oo 


jT 


< < 


t- 


a. CJ 


UJ 


Q 


00 




MM 


(X 


H- O0 


< 


^ UJ 


UJ — 


UJ X 


Z 


* cj 


— UJ 


uj z 


-1 oo 


u ■— 


« 


< — 


t_> 


_) 




a. o 




oo z 




•- 3 




a u 


_l 


ac 


< o 


UJ o 


3 « 


> 


►- oc 


— c-> 


U UJ 


►- z 


« 


< < 




_J 




UJ oo 




a oo 




< 




Z X. 


o 


3 


o < 


Z 


Z rx 


** 


a 


X 




< 




z 





oo O 

< Z 



• ai 
a o 



o o o c o 



— co m ^ in 



t— CO CO o c- 

c- o? c- 03 an 

IT. CO >t 0)- O 

o*o»o 

C 00 f> c o 

• t • • • 

O O O O ^ 



^ oo co o o* 1 
IONSOO 
r-* 00 -Of 03 O 
— 1 rl CO O O 

o o o o o 



o* co o< c r* 

ITS ^3 f^ CO «-t 

c- <<■ in r- o 

O lf> 03 C- O 

O* 00 00 0* 1 © 

• • • t • 

o o o o .-< 



oo in co 03 03 

in co oj oo ,*■ 

oo in oo o in 

O" >t (M (MT 

oo r- co co t-i 

• • • • • 

O 0" oo oo r- 



o co co co o 
<-i m o o- v 
co o >t in a> 
r- <r co oo «i 

• • • ■ 9 



O 00 CO 00 03 
CO CO ^ 00 CO 

co ■*" in m o* 

n Bom o 

ONNffK- 

• t • t t 

i\io(M)h 



■4* r- o> r» 03 

co oo Co co o 

OO CO f- O 00 

m o co co of 

co co o3 in f-< 

• • • • • 

ci co o oo r- 



-h co co oj- m 



m 03 r- 


.-■ r- 


■* f* o> 00 


^. 




O O co 


co O 


ir ec o> * 


p-* 




r- c- f 


CJ CO 


— > m it 03 


■-0 




>* or\ Ji 


oD <\i 


c oo co m 


in 




co m oc 


C m 


m co —> •* 


CO 




• • # 


• • 


9 • 9 • 


t 


UJ 


o o o 


»— * ■-- ' 


-^ CO IT 03 


OO 


o 
or 

D 
u. 

O 


— • co m 


>t m 


^- (\J re N* 


oo 


«r 



-*■ >t c- co in 

f- V- r- O •— 

a> •* •* ~-< -t 

CO C". 00 Cl 

o~ O O O — ' 

t • • • • 

O «— • •— i •-• — ' 



»-• 03 co in o 

^* 03 C- s 0o 

OO O 00 00 o 

ShOO^ 

a o © © o 



moon o 

in in © cm f- 

r- in ,-< ,< 03 

oo © o oj —> 

r^ o v o^ f- c- 

• • t • • 

o o o o o 



>© C- ,»■ CJ 03 

O oo ro m oo 

00 03 •of- 03 © 

r- ir. m co no 

—* m 03 oo ao 

• • • • • 

m o)- 9- c- sf 



s s oo CI CC 

^^ 03 03 © Co 

>0 © 03 Of O 

-C 03 Of 03 OC 



C Of OO O »-l 
CO O) CO 00 c> 

in of -o © >o 

rtrl-'HN 

o © o o o 



co oo o oc cm 

O en ro cr CT- 

03 »-» oo cm m 

c- cc a c- 03 

r- c- r- c- r- 

• • • • • 

o o o © o 



CJ CO — 03 CO 

03 O Ci Oo O 

03 c- oo in —< 

Cl CJ* 9-* 03 03 

c\j -< ci — of 

• • • • • 

03 UO Of CI 9" 



< 



o 

a 



of in 


<-H 


c- 


9-t 


Of 


<— i 


CC 


cr 


•o 


t- 


— 


OJ CI 


CO 


03 


in 


<1 


CM 


r- 


cm 


--* 


3 


-i 


C- IT. 


o 


of ci 


o~ 


CM 


co 


a 


r-4 


a 




9-9 *— ' 


03 


O f- 


CO 


-* 


o 


o; 


C- 


z 


o 


O CO 


CI 


co 


of 


Of 


UO 


CO 


c- 


co 


CJ 


t- 


• • 


• 


• 


• 


t 


• 


• 


• 


f 


o 




Ofl Of 


rH 


c- 


»* 


UO 


o; 


Cl 


CM 


9-9 


9— 


o 


f-0 t-M 


•-I 
















00 

oo 


UJ 

oi 


of m 


or 


•c 


Oi 


UO 


Cl 


CM 


CM 


03 


< 




— * 


UO 


CO 


o 


ou 


UO 


o 


CU 


CO 


z 


O0 


aj oo 


CM 


Of 


r- 


r- 


r^ 


03 


o- 


f- 




*- 


OT Oy 


>C 


Cl 


a 


o? 


r- 


OJ 


—9 


Cl 


X 




-H O 


CM 


CM 


CO 


CO 


Of 


r- 


c- 


CO 


o 


> 


• • 


t 


• 


# 


• 


• 


• 


• 


• 


^ 


r- 


U> Of 


•-* 


r- 


Of 


UO 


Of 


Cl 


CM 


--* 


UJ 


•— 


9-9 9-9 


■"" 
















u. 
O 


o 


•* fC 


0* 


•-* 


00 


Of 


r- 


u- 


oo 


UO 




UJ 


co co 


O in 


CO 


CO 


CM 


co 


o 


f— i 


>■ 


> 


r- co 


o 


Cf 


in 


9-9 


o 


03 


o; 


03 


1- 




O Ci 


o 


o o> 


<r 


Cl 


c- 


#-H 


,— j 


|^4 


a 


co u" 


UO 


UO 


CJ' 


00 


r- 


f- 


u> 


<C 


O 


z 


• • 


• 


• 


• 


• 


• 


t 


t 


• 


o 


_> 


CJ> UO 


CM 


C 


UO 


03 


UO 


Of 


Cl 


■M 


_l 


CJ 


W9 ^4 


»-4 
















UJ 

1 

t— 1 


o 
i 

CO 


— i ro 


Cl 


O) 


UO 


•-i 


CM 


Cl 


>J 


UO 


UJ 
oo 

< 
o 


UJ 

oo 

< 

CJ 



ac < 
u. a 



117 



U cm 

_j o lu 
3 «- «/> 

< h- < 

a 

>- 

1 o 

z 

0C ^- f-4 

< a 

Oil UJ 

Z < to 

p~ G < 

_l !_■ 



•» a * it, oc 

eo ro -c h- co 

f- ro eo cm m 

Cr *t CM CM ^ 

o o o o o 

• • • • • 

o o o o o 



ao t-< f-4 in r~ 

*■ •*■ m m «\j 

cm <«■ cr f- m 

O O O O O 

• • • « • 

o o o o o 



eo ^ m cr od 

or o -O -O m 

it r- 4 fnv/ 
-< o o o o 
o o o o o 

t • • • • 

o o c o o 



CM gj -C O 00 

m r- ■* eo cm 
— o o o o 
o o o o c 
• • • • • 
o o o o c 



t-i gj r- p-< CM 

gj •-« f- gj ^f 

cm — i o o o 

o o o o o 

o o o o o 

t t t • • 

o o o o o 



noc 4- co a 

CNI 00 CM CT «0 

•J- ^ — i O O 

o o o o o 

o o o c o 

• • • • • 

o o o o o 



Q 

a 



<y to 

a. a. 
ex o 





+J 




E 




a> 




E 




O 




Q. 




E 




O 




o 




cr> 




1 

2: 




"LO 




O O 




«* • 




cr> 




r— II 




n 




a> qq. 




JMS 




CO 




13 • 




cr e 




je 


r«^ 


+-> T- 


i— 


S- -M 


• 


CO 3 


CO 


UJ ( — 







QJ 


O C/j 


r— 


s_ 


jO. 


-M E 


CO 


E O 


I— 


O) -r- 




4-J 




CO 




1— t- 




LU O") 




<u 




+-> 




+-> E 




1— 1 




nz 




^f- +j 









E 0J 




CU S- 




4-> t- 




CO Q 




>> 




00 



ON(MMIfl 
t-i «t 00 ■* O 
o O gj cm r- 

OOmhcm 

■ • • • • 

OOOOO 



m gj r» •-• r- 

o o f> co o 

t" r- CO cm cm 

<t m .4 gj cm 

cm in 00 o m 

• • • • • 

© o o — ~* 



•4 t-i cr oo •— 

ir cc o~ <; -1 

H IT ITi 4 rt 

o 00 cm if m 

• • • t • 

»-< ro m g; cr 



t/i 

E 
O 
Q- 
10 

O) 

a: 
















































z 


#-■ 


M 


f 


■* 


in 


»-* 


r^. 


c, 


<x 


in 


r-< 


CM' 


r> 


4 


if 


< 






X 




4 
































oc 


UJ 

I 
t- 






"V CX 


4- 


■C 


(\J 


n 


—* 


r- 


r-k 





CM 


m 


a 


O 


r- 


<\J 


f< 








CM 





O 


•— « 


>o 


>o 


r- 


o> 


p-H 





O 


u- 


cr 


CM 


in 


r- 


a 


Ul 










a 


m 


a 


(7- 


W-* 


r- 


fNJ 


rn 


r>- 


O 


r- 


P» 


r- 


cr 


r- 


rg 






UJ 


-J 





a 


o- 


0* 








CM 


<SJ 


CM 


p*i 





O 





^-* 


f-H 


PM 






to 


< 


o- 


00 


0- 


o- 





cr 


c 





O 


O 


c 


O 





c 


O 


CL 






< 


3 


• 


« 


t 


• 


t 


• 


• 


• 


• 


• 


t 


• 


• 


• 


• 


<l 









p- 
O 











O 


•— ( 







*-< 


*-* 






—^ 


-H 


*-> 


»-( 


UJ 

z 
_J 




UL 




O 





































O 


V. 


<r 


•-< m 


>o 


in 


r>- 


O 


\r 





IT 


Cr 


r- 


•* 


•J 





00 


K 




tO 


pH 


or 


a 


m 


a 


ac 


CM 


o> 


cr- 


C7~ 


X 


•«• 


r- 


in 


a- 


<E 


ao 






z z 




O 


•* 





a 


a 


O 


r-- 


pnl 


ri 


•& 


O 


i-C 


~-< 


p*i 


00 


r- 


O 







UJ 




*-« 


~* 


o- 


O 


O 





fV 


CM 


t\* 


^» 





O 





O 


O 


UJ 




1/1 _, 


10 


_J 


O 


O' 


c 


O 


a- 


O 





O 


O 


c 


O 


c 


O 


O 


00 




1— p- 


< 


< 


• 


• 


• 


• 


• 


• 


t 


• 


• 


• 


• 


• 


• 


• 


• 


3 




or 3 


l_) 


r> 


r* 


,-« 








_. 





r-* 


•— i 


*4 


•-1 


,— 1 


f-H 


p4 


.— t 


,_~( 






< _l 




t- 
































10 




a 





































•— 1 




1 to 




< 




































O 




































«-» 







>v 


































X 






O 




r~ 


rri 


— . 


rs; 


in 


r- 


O 


ac 


CM 


n 


cr 


^ 


•-h 


~c 


m 


UJ 






< 


<4> 


m4 





pM 


O 


»!■ 


f. 


IT 


00 


vf 


c. 


>o 


a> 


ip 


eo 


or 


_J 






a. 


< 


#— « 


in 


O 


O 


O 


-* 


00 


IT\ 


O 


ro 


e'- 


ro 


ro 


CO 


^; 


00 


UJ 







ac 


"1 


O 


ao 


O 


O 


•C 


*4 


^H 


PH 


f- 


er 


a 


ac 


v0 


•0 





l_) 






O 


O- 


a 


a- 


O 


O 


a 


c~ 


o- 


a 


0- 


cr 


CT 


<T 


CT 


cr 


ox 


ac 




—1 




• 


• 


• 


• 


• 


• 


• 


• 


« 


• 


• 


• 


• 


• 


• 


a. 


O 




< 


O 


O O 





r— 


w* 





c 





O 


c 


O 


O 


O 







LL 




3 


Z 
































CJ 






p- 


































< 


O 




O 


































a. 


< 




< 


































O 


or 

c 

UJ 








O 


(<- 





-c 





r-- 


tv; 


pH 


~o 


CM 


r- 


r- 


(O 


r- 


CO 


3 


X 






CM 


r- 


in 


<f 


vn 


0- 


CM 


CM 


-* 


v> 


CM 


r- 





f- 


O 


-4 


1- 


r- 


z 






fH 


a- 


*-~> 


•Hi 


CM 


m 


ao 


a- 


m 


m 


m 


in 


CM 


CO 


CM 







UJ 




UJ 


r- 


m 


(M 


^ 


^. 


CM 


* 


m 


r- 


<t 


r- 


sO 


CO 


•c 


H 


< 


Ul 


UJ 


O 


l/l 


m 


t\j 


rg 


^^ 


cr 


00 


m 


CD 


r-4 


*— i 


cr 


(NJ 


~c 


ar 


cr 




►«J 


» 


< 


< 


• 


t 


• 


• 


• 


• 


• 


• 


• 


• 


t 


• 


• 


• 


• 


Z 


— . 


K 


tc 


O 


00 


00 


00 


CO 


O 


tn 


(M 


cr- 


O 


m 


CO 


m 


IN) 


H 





■— 


OC 


111 


O 














t-H 


ft 




















f 


CD 




































O 


UJ 


p» 


at 


































UJ 


z 


»- l/l 


< 




*_« 


00 


C 





cn 


Cf 


»-» 


<f 


in 


cr 


in. 


vf 


CM 


CO 


m 


r- 


— 


2 UJ 


UJ 


f-* 


O 





CM 


•* 


cr 


CM 


n 


00 


>r 





m 


r- 


O 


CM 


•* 


3 


— 1 


UJ X 


z 




O 





-» 


fl 


CM 


CM 


^D 


r- 


v) 


CO 


co 


~o 


00 


r"i 


cr 


a. 




X O 


Ml 


UJ 


r» 


CM 


CM 


-1 


^-* 


CM 


^ 


ro 


r- 


4 


in 


vT 


t—4 


* 


O 


X 





uj z 


_J 


to 


m 


tn 


CM 


^H 


a- 


CO 


m 


ao 


pH 


-* 


cr 


CM 


O 


ac 


cr 





p- 


— 




4 


• 


• 


• 


■ 


• 


• 


t 


• 


t 


• 


• 


• 


• 


• 


• 







< — 




<_> 


o> 


tr 


00 


00 





O 


(M 


0- 


~o 


CO 


c 


P> 


(V. 


rH 





««• 





_! 
















pH 


W-* 




















UJ 


O. O 




































to 


00 


to z 




































1/) 


-> 


— 3 






r~ 


r- 


a 





r- 


r- 


m 


Cr- 


ao 


-0 


00 


-» 


J- 


^ 


00 


< 




u 


-J 




fO 


<— 


>» 


<o 





m 


t«t 


in 


cr 


■* 


in 


r~ 


cr 


O 


CO 


X 


•/) 


ex 


< 


O 


o> 


m 


-J 


«t 


•-1 


t-4 


.— 1 


r^ 


CM O 





•— * 


CM 


r- 


•a 




»— . 


UJ CS 


3 «» 


CM 


rj 


CM 


>* 


t-i 


in 


00 


^^ 


p«l 


~ 


•t 


«*■ 


f-l 


CM 


o- 


X 




> 


P- 


a 


•* 


»SJ 


CM 


*-* 


o> 


CO 





>CJ 


O 


f— 1 


cr 


CM 





00 


00 





>- 


— l_ 


u 


i_i 


• 


• 


• 


f 


• 


• 


• 


• 


• 


• 


• 


• 


• 


t 


t 


«i 


p— 


►- z 


« 




u* 


IT 


UJ 


00 


<o 


fn 


CM 


cr 


■c 


CO 


CO 


tn 


INI 


p^ 





UJ 


pp 


< < 
















ih4 


•-H 























_l 




































u. 





UJ to 







































_l 


or 10 






CM CO CM O CO 


CO f~ 


O 





CO 


>r 





m 


•* 


CM 




UJ 


< 






C*» 


— * 


-*■ 


^ 


«)> 


p^ 


O 


0- 


^ 


-0 








r- 


in 


r-4 


> 


> 


x x 




O 


<0 


rA 


r-* 


<*■ r- 


c> 


r~ 


O 


-* 


m 


CM 


in 


-0 


m 


r- 


t- 




3 





< 


CM 


cr 


O 


«» 





<0 in 








cr 


r~* 


cr 


m 


cr 


CM 


t-t 





2 


z 


ct 


pal 


w-4 


f\ 


•— 1 


cr> 


CO 


»— < 


in 


■£> 


*— < 


O 


CM 


<o 


ao 


cr 





z 


** 




O 


• 


• 


• 


■ 


• 


t 


• 


• 


• 


• 


• 


• 


• 


• 


• 





3 


X 






O O 


00 


03 


<0 


<*■ 


m 





■& 


co 


>» 


n 


(NJ 


~* 





-J 





< 






p4 


*-* 








•-• 


f-H 


i-t 
















UJ 


QL 


X 




































> 
1 


19 

1 



l/> • 
l/> o 
«» z 



• UJ 

00 



ex < 

u, oc 



— 1 cm ro -3 in 



t-i cm co .* m 



ph cm ro >» m 



i/> to 

< < 



118 



CO 

ro 

CD 
CO 



+-> 




c 




QJ 




c 




o 




Q. 




E 




O 




o 




co 




1 




#\ 


, 


o 


o 


^t- 


• 


C7. 




•— 


II 


r- 


CO 


O) 


GO. 


-^ 




03 




Z5 


• 


O" 


SZ 


-C 


O 


4-> 


•.J - 


S- 


4-> 


fO 


3 


LU 


r— 




o 


o 


oo 


s- 




-t-> 


c 


c 


o 


CD 


•1— 


o 


4-> 




fO 


r— 


s- 


LU 


o> 




CD 


o 


+-> 


+-> 


£Z 




I— I 


3C 




LO 


+-> 




O 


E 


cd 


CD 


s- 


+-> 


•1" 


to 


o 


>1 




co 







o 




P0 


<m a oo .4 


OD 


oo p- <C m or 


houo^ 






»-4 






r- <* cr .- 


00 


oo <o •-) o <vj 


«H«IM^ 






_J o 




UJ 


O«0H 


in 


m <*D <* pn Pj 


MhOoo 






D — 




to 


-4 •♦ CSJ (VJ 


-~* 


*■• o o o o 


o o o o o 






< r- 




•a 


-• o o o 


o 


o o o o o 


o o o o o 






a < 




u 


• • t • 


• 


• • • • • 


• • • 4 • 






of 

> 

1 o 






O O O o 


o 


o o o o o 


o o o o o 






















z 
















to 


a •- 




#— t 


(M OD a m 


00 


p- cr •» •* •* 


—i .-« -4 PJ «C 




UJ 


< a. 






r- in © wo 


o- 


•-H 00 m O O 


4 ~* O- «* O 




•— ■ 


UJ X 




UJ 


* -t c>c 


•* 


t-< od in «*■ ro 


p- m •-< <-i r* 




>- 


z < 




I/O 


(HhOO 


o 


cvj o O o C 


o o o o o 




a 


— c 




< 


o o o o 


o 


o o o o o 


o o o © o 




UJ 


_l 




o 


• •ft 


• 


• 4 • • • 


• • • • t 




a 
o 

cc 
a. 








o o o O 


o 


o o o o o 


o o o o o 






• 


,_ 


^j O °° ao 


in 


in o o* o <\j 


■f I 4 oo ir. 




_i 




o 


1/) 


•4" ><■ pn in 


O 


O ^N OOM 


m CM C> <C PNJ 




< 




UJ 


a 


m «sr m m 


p- 


p- od m rri pj 


h ^ O 1^1 CO 




o 




or 


u 


ft OD PO oc 


•4 


•4 00 >4 CP PVJ 


o r- m »o <•£> 




o 




U- 


— » 


O © •-< ■-• 


pj 


PJ in CT PJ P 1 - 


KMT MO 4- 




x 








• • • • 


• 


• • • t • 


t t • • ■ 


UJ 










o o o o o 


o o o .-. -> 


-* pr ir. r- O 


U 
















" H 


at 
O 



CD 
to 

c 
o 

Q. 

to 

CD 





UJ 


• 




































a 


o 






























c 






o z 


i-< r\j 


l«1 


•* 


in 


r-* 


(M 


rr 


4 m 


*-* 


p 


m 


-1 


in 


•a 






X 


< 






























of 

O 

UJ 

I 
t— 






>» 


oc 


on © od 


*-< 


00 


00 


<h 


mt 


« 


#— * 


•c 


00 


^^ 


P- 


•4- 








fSJ 


o 


o> .-* 


^J 


•-H 


* 


00 


«— i 


-C 


-* 


00 


o- 


p- 


rvj 


C0 


ITi 


UJ 










<o a 


a 


o- 


O 


p- 


^ 


4 


CO 


•fi 


m 


^0 


CM 


p- 


PP. 


rvj 






UJ 


_1 


o c 


a 


a 


o 


-» 


4 


4 


4 


o 


m 


-o 


o- 


oc 


ao 


tm 






oo 


< 


cr o- 


ty 


o- 


o 


o e 


O 


O O 


w* 


mi 


r-4 


--* 


mi 


or 






< 


D 


• • 


• 


• 


• 


• 


• 


• 


• 


4 


4 


4 


4 


4 


4 


•a 






o 


o 

< 


© o 


o 


o 




*-« 




^- J 


^-< 




W-* 


*-* 


*-" 


m> 


•M 


UJ 

z 

_l 




u. 




o 






























o 




o 


v> 


< 


NO'S 


oo 


CO 


^m* 


00 


o- 


s0 


CP 


0> 


cr 


>» 


00 


o 


t- 




to 


^4 


oc 


m ^> r^ 


>0 


o 


f»> 


Pv 


<f 


p- 


p-v 


m 


^) 


oo 


•£> 


o 






z z 




o 


o o> 


c 


er 


O 


«» 


<N 


rvj 


in 


in 


p- 


cr 


a 


•t 


«* 


o 




o o 


UJ 




o o 


0> 0- 


o 


Po 


INJ 


Psl 


py 


cr 


00 


CO 


w~* 


■-» 


ml 


UJ 




to ■— 


to 


_J 


o o> 


<y 


a 


o 


o 


o 


O 


o 


a- 


cr 


cr 


o 


o 


o 


to 




«-4 0- 


< 


4 


• • 


• 


• 


• 


• 


f 


t 


• 


4 


4 


4 


4 


4 


4 


3 




CC o 


<_> 


3 


— o 


o 


o 


t-l 


.-I 


^^ 


•-i 


^^ 


o 


o 


o 


•— » 


•-» 


— < 






< -J 




1- 






























to 




o. o 




(_> 






























p— • 




X </> 




< 


































a 


































mm 




o 


"V 
































X 






t5 




j- a 


00 


h- 


M 


<M 


oc 


ro 


o- 


4 


m 


o 


^0 


vO 


cr 


LU 






< 


o 


iri r- 


<o 


a 


o 


m 


ac 


po O 


oo 


CO 


p4 


IT' 


PJ 


•o 


-J 






OL 


«I 


00 IT 


m 


cr- 


o 


O 


-* 


P- 


rg 


-o 


P( 


t) 


-J" 


-o 


cr 


00 


LL 




o 


ac 


ir> (si 


^-t 


cr 


o 


a 


0> 


o- 


o 


r\j 


00 


p- 


in 


in 


m 


c 


o 






o 


od a 


» 


a 


o 


cc 


ac 


00 


oc 


oo 


p- 


p- 


p» 


P- 


p- 


OL 


or 




_l 




• • 


• 


• 


• 


• 


• 


* 


i 


4 


4 


4 


• 


4 


4 


a 


O 




•* o 


o o 


o o 


w* 


o 


o 


o o 


o 


o 


o 


o 


o 


o 




LL 




3 2 






























o 






►- 
































i 


o 




U 
































or 


<t 




«l 
































o 

< 


ac 

a 

UJ 








>o .»■ 


•* 


^^ 


m 


IT 


.0 


<\J 


rr, 


•c 


«»■ 


o 


0- 


c 


*H 


2 


I 






CJ 


-• o 


•-< 


r- 


in 


P- 


<t 


v-4 


o- 


00 


ir\ 


p- 


<f 


o 


p— ( 


►- 


(- 


z 






>»■ <^ 


r-( 


a 


r\ 


«*• 


INI 


>!- 


CP 


* 


p- 


m 


^-< 


o 


a 


o 




UJ 




UJ 


m <r\ 


rn 


o 


00 


o o 


a 


in 


p- 


m 


in 


a 


-* 


er 


< 


UJ 


UJ 


O to 


m tr\ 


l«1 


m 


in 


ro 


OC 


>o 


o- 


o 


p- 


m 


IT 


in 


o 




PJ 


jt 


< 


< 


• t 


• 


• 


• 


• 


• 


• 


• 


• 


4 


4 


• 


• 


4 


z 


— - 


t- 


ae 


<_) 


ao ao 


eo 


00 


r- 


m 


m 


#-* 


0D 


in 


in 


ir 


•* 


m 


t-4 


1— 1 


ac 


UJ 


o 












t-* 


,-t 


•-* 


















i 


03 


































a 


UJ 


•** 


or 
































UJ 


z 


»- VI 


< 




<o ffl 


(m in 


<\! 


4 


00 


ir> 


Pvl 


oc 


<C 


sC 


mi 


mi 


U, 


t- 


1— 1 


«I UJ 


UJ 


»-t 


ir\ ^ 


o 


4 


O 


in 


4 


4 


CP 


po 


p- 


mi 


o 


•£l 


P- 


3 


_l 


UJ i 


z 




r^ r~ 


<0 4 O 


o o 


>o 


m 


cr 


00 


mi 


m 


4 


PJ 


a 




x u 


N4 


UJ 


o^ t*\ rn 


«-4 


00 


o o 


4 


-o 


i-t 


mi 


4 


cr 


PJ 


mi 


X 


o 


UJ Z 


-J 


(O 


0D fTl 


ro 


m 


m 


cr 


m >t 


p- 


o 


cr 


m 


00 


O 


P- 


o 


K 


O "• 




< 


• t 


• 


• 


• 


• 


• 


• 


* 


4 


4 


1 


4 


4 


• 


u 




•* — • 




(_> 


OD OO 


00 


ao 


r- 


-»■ 


pn 


<— t 


oc 


m 


•»• 


•J 


m 


m 


■>-4 


w 


© 


ml 














mi 


W-* 


.— < 


















UJ 


a u 


































to 


to 


wl z 


































to 


_> 


— z> 






0* f^ 


>» 


a 


r- 


o 


o- 


p- 


CD 


m* 


a 


•t m p. 


o 


< 




oo 


-J 




O ID 


0> 


o 


au 


* 


PJ 


5 


P- 


m 


m 


>»■ 


Po 


at 


— 1 


X 


oo 


ac 


< 


o 


4- O t^ 


f- 


v> 


in 


•AJ 


m 


rg 


o 


oc 


—i 


tj 


CP 




•— ' 


UJ o 


3 •« 


o» ^> 


m 


t-t 


r- 


o o 


cr 


•f 


•»■ 


00 


ao 


u '. 


ac 


00 


I 




> 


»- OC 


oo m 


n 


m 


m 


<c 


PJ 


#-• 


m 


o 


cr 


m 


ao 


tr 


<0 


<_> 


> 


— u 


u 


u 


• t 


* 


• 


t 


• 


• 


4 


• 


4 


4 


4 


4 


4 


4 


•« 


f— 


►- z 


•Jt 




ao ao 


aj 


au 


p- 


•»• 


n 


~* 


00 


in 


•r 


J- 


m 


PJ 


mi 


UJ 


mi 


< < 














f»4 


p~< 


--> 


















O 


_) 


































u. 


o 


UJ to 


































o 


-J 


or oo 






r- r~ 


00 


■£> 


00 


CP 


>r 


cr 


m 


«»• 


pj 


CC 00 


PJ 




UJ 


4 






<M O 


<o 


r?\ 


r» 


a- 


IT 


00 


sf 


m 


m* 


mi 


cr 


•c 


•4- 


> 


> 


X X 




o 


o 0» 


«r\ t>- 


o> 


o 


p- 


>o 


CP 


au 


CM 


PJ 


PO 


mi 


n 


>- 




r> 


o 


< 


o o 


<VJ 


•-* 


r- 


o 


in 


p- 


P- 


a 


O 


w4 


o 


-*■ 


pj 


kwl 


o 


X 


z 


ac 


fO o 


•-< 


CO 


m 


-t p- 


4 


m 


<_> 


PI 


o- 


rH 


cr 


r\i 


o 


z 


^^ 




o 


• • 


t 


t 


• 


t 


• 


• 


4 


• 


4 


4 


4 


4 


• 


u 


3 


X 






o o> 


o 


00 


p- 


<e 


•* 


PW 0* 


-c 


•o 


m m f> pg 


-J 


o 


< 






«-4 








mi 


mi 


>-4 
















UJ 


a 


X 


































> 


o 



tO 4 

to O 

< Z 

X 



i-i r\i 



m> pj m 4 in 



h rg m j in 



•-j pj pi <sf in 



4 UJ 

a o 

uj z 
ec < 



m 



119 





4-> 




C 




<u 




c 




o 




Q. 




E 




O 




o 




oo 

1 




1 




"in 




o o 




^- • 




cr> 




r— II 




« to 




(D CO. 




-if- 




ra 




3 • 




cr c 




-C o 


<Ti 


+j •!- 


i — 


S- 4-> 


• 


rt3 ZJ 


OO 


UJ i— 




o 


QJ 


o oo 


r— 


S- 


-O 


+-> c 


rO 


sz o 


1— 


0) -r- 




o +J 




(TJ 




i— s- 




LU O) 




CD 




O -(-> 




-»-> c 




1— 1 




nz 




LO +-> 




u 




E Ol 




CD S- 




4-> T- 




to Q 




>> 




oo 




l+- 




o 




<u 




c/> 




c 




o 




O. 




V) 




cu 




ct. 





u 




CM 


Na e <r on 


oo f- «d co as 


_ 


OtOr- 




P-t 






h" <# O p-t 03 


ec »c h o cm 


■0 


P-t 


«0 IT CO 




-I o 




UJ 


O * oo — m 


m «o *• co tv 


cm 


ppj 


o o c 




3 — 




«/> 


—< <t CM CM —i 


-« O O O O 


o 


c 


O O c 




< *- 




•a 


— i o o o o 


o o o o o 


o o o o o 




at < 




U 


• • t • • 


• • • • • 


• 


• 


• • • 




O C£ 

>- 

X o 

z 






o o o o o 


O O O O c 


o 


o 


o o o 


















«/> 


a ►- 




•-i 


HOireo 1 


IT' co p- co o 


00 


w~* 


tf> ih c 


UJ 


< a 






o m ir r- tn 


«* co if* fri it 


r- 


c 


CM o> <o 


p-i 


UJ X 




UJ 


iro«^ci 


f- p- «» co tv 


«t 


CM 


— o o 


»- 


z < 




i/) 


CM —i o c o 


•-" o o o o 


o 


c 


o o o 


0L 


"- c 




< 


o o o o o 


o o o o o 


o 


o 


o c o 


UJ 


-J 




o 


• • • • • 


• • • • • 


• 


• 


• • • 


a 
o 








o o o o o 


O O o o o 


o 


o 


o c o 


ex 

a 




• 


„ 


^ o eo a> m 


Kl OOON 


^ 


oo 


-O 00 in 


-J 




O f> 


^4 nmo 


o ^t r- oo «*» 


in 


rv 


ro -d cm 


< 




Uj 


a. 


it <>/ in vi h 


p- ao co c cm 


r-t 


*c 


<f ' co oo 


c 




Dl 


o 


CO CD CO 00 4 


•4- op •* o> c\) 


o 


r> 


CO sO ^ 


o 




u. 


w 


OOhhN 


rvlifi f/ mn 


IT. 


IT 


r- ao .* 


x 








• • • • t 


• • t • • 


• 


• 


• t • 



o o o o o 



© O O -• >-> 



—i m in t- O 





a 


O 
































o 






o 


z 


^-« 


CM 


IT 


sr 


in 


*-• 


CM CO 


-» 


in 


•— « 


CM 


tri 


~t 


in 


< 






X 


< 
































cr 

Q 

Uj 

I 
r- 






^» 


ec 


«»■ 


<0 m 


a 


^4 


o> 


ro 


a 


CM 


a> 


CM 


m 


o 


CO 


c 








(M 


o 


»NJ 


d 


IT 


^t 


ao 


CM O 


ro 


CM 


«t 


r- 


r- 


o 


~c 


a 


Ul 










t> 


a 


a 


IT 


o 


m 


CM 


CM 


in 


^> 


s 


a 


o 


c 


m 


PSI 






UJ 


-J 


o> 


a 


a 


O- 


o 


CM 


CO 


CO 


CO 


o 


o 


O 


*—i 


r-4 


CM 


»-• 






l/> 


< 


0> 


0* 


Ch 


C7- 


o 


o o o o o 


c 


o 


o 


O 


o 


cc 






< 


3 


• 


• 


t 


• 


• 


t 


« 


• 


# 


• 


• 


• 


1 


• 


• 


•I 






O 


1- 


o o o o 


i-i 


f-t 


r-* 


-H 


■~i 


-~* 


■-» 


*-* 


w-t 


—4 


PH 


UJ 








O 
































z 








«* 
































_) 




u. 




o 
































C 




o 


■V 


< 


•*• 


IT- 


o- 


r>« 


-0 


ftH 


to 


-0 


CM 


^~ 


r~* 


00 


m 


o- 


e> 


r- 




to 


p4 


a 


h- 


oc 


a 


00 


o 


ao 


~c 


o 


r- 


in 


CO 


CM 


>r 


a 


<o 






z z 




o 


o- 


» 


o- 


O 


o 


00 


m 


o 


cc 


*-* 


CM 


CM 


CM 


CM 


P-4 


o 




o o 


UJ 




t> 


0> 


» 


o- 


o 


•"-» 


CM 


CM 


CM 


o 


O 


O 


O 


O 


r-H 


UJ 




</> •— 


to 


_i 


f> 


o- 


a- 


0- 


o 


c 


C 


o 


o 


o 


O 


O 


o 


O 


o 


to 




1-4 r- 


< 


< 


• 


• 


• 


• 


• 


t 


■ 


• 


• 


• 


t 


t 


• 


• 


• 


Z3 




oe D 


o 


D 


o 


o o 


o 


—1 


t-4 


f~* 


~-* 


pa| 


-H 


w~4 


^ 


#-) 


•-4 


■-I 






< -I 




H 
































to 




o- a 




l_) 
































•— 




X to 




< 




































o 




































<-• 




«_> 


'v 


































X 






o 




M 


•— 1 


a 


4 


CM 


o 


in 


or. 


o 


^3 


in 


in 


r-4 


a 


in- 


UJ 






< 


O 


m4 


o 


CD 


o 


CM 


CC 


ro 


ao 


O P- 


in 


4 


•— < 


rj 


•* 


-1 






cc 


< 


o 


o 


0> 


o 


O 


>*■ 


a- 


O 


•0 


in 


#— ' 


t— i 


r-t 


o 


ao 


00 


UJ 




Q 


a. 


o o 


a 


o 


o 


pH 


o 


o 


o 


<C 


ao 


ao 


00 


cc 


m 


o 









O 


o o 


o 


o 


o 


tr 


<T 


0- 


o- 


o- 


o- 


a 





o- 


0- 


or 


cr 




_J 




• 


t 


• 


• 


t 


• 


t 


t 


• 


• 


• 


• 


• 


• 


• 


a. 


a 




< 


c 


■H 


w-A 


o 


i— 1 


^H 


o 


o o 


o 


o 


o 


o 


o 


o 


o 




IL 




D 


z 
































o 






1- 


































«i 


o 




o 


































or 


< 




< 


































o 

—i 

< 


CX 

o 

UJ 








r»> 


^0 


<r 


^~ 


«t 


r- 


in 


r- 


cr 


a 


o 


CM 


rv 


ro 


p- 


o 


X 






<NJ 


r~ ITi 


a 


•— 


m 


<C 


>—i 


•— i 


r- 


oc 


r- 


r-~ 


CM 


rj 


•c 


H 


p- 


z 






o 


* 


a 


CO 


CM 


ao 


O 


~0 


p- 


o> 


in 


Ci- 


N» 


CM 


CM 


tJ 




UJ 




UJ 


•0 


in 


r^ 


CO 


00 


O 


m 


CO 


in 


o> 


m, 


p- 


m 


ro 


•* 


< 


u. 


UJ 


o 


in 


f\J 


r\i 


CM 


—* 


m 


IM 


O 


~-4 


■o 


CM 


<C 


ro 


CO 


•-4 


CM 




rsj 


X 


< 


■a 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


1 


• 


z 


»-^ 


»- 


or O 


ao 


CO 


co 


CC 


t^ 


CO 


CM 


o 


r- 


* 


CO 


to 


CM 


CM 


w* 


»*4 


or 


UJ 


a 














*4 


w~* 


1— 1 


















< 


ffi 




































o 


UJ 


pp» 


ae 


































LU 


z 


»- l>0 


< 




0- 


•^ 


r-l 


o 


m 


m 


r-i 


CM 


|h4 


C^ 


•0 


CM 


•0 


a 


IT. 


r- 


•— ' 


Z uj 


UJ 


w* 


■ 


>c 


CD 


CM 


O 


•— » 


>»• 


r- 


p- 


CM 


oc 


*-i 


ao 


a 


* 


3 


_J 


UJ X 


z 




«»• 


co 


c«i 


—t 


h- 


in 


in 


f 


o- 


r- 


a 


•J 


CM 


IT 


m 


a 




X O 


•-^ 


UJ 


<0 IT) 


>t 


a- 


P«- 


CM 


r- 


CM 


O 


X 


CM 


in 


ro 


*-* 


CM 


X 


o 


UJ z 


_l 


to 


fM 


CM 


CM 


^H 


Cl 


w* 


c* 


f— t 


^0 


CM 


•o 


CO 


ao 


*— • 


CM 


o 


t- 


O "- 




« 


t 


• 


• 


• 


• 


• 


• 


• 


• 


t 


i 


• 


• 


• 


• 


o 




< — 




u 


OO 


0D 


CO 


ao 


r- 


CO 


•— « 


o 


r- 


•»• 


co 


CO 


CM 


CM 


— * 


MMi 


C-J 


_J 
















IM 


pH 


•— I 


















UJ 


a a 




































to 


to 


to z 




































to 


-J 


— 3 






«»■ 


CM 


r» 


r- 


o 


>» 


--^ 


CJ 


r- 


K 


•-4 


re 


m 


o 


O 


<r 




O U 


_J 




O 00 


00 CM O 


0B 


*~* 


s0 


CM «0 


ui 


-t 


a 


•o 


CO 


X 


to 


QC 


< 


c> 


r- «r 


fO 


CM 


•*> 


CM 


~U 


^) 


r» «3 


O 


~c 


u\ 


cr 


f— > 




•-• 


UJ to 


3 


< 


«ir*o>h 


00 


t~- 


* 


a 


00 


CM 


<t 


CM 


o 


>-< 


I 




> 


t- 


a 


r\j rvj (\J 


•— » 


co 


ao 


<1 


aj 


CO 


CM 


<o 


ro 


cc 


r-4 


CM 


o 


> 


M U 


w 


u 


• 


• 


ff 


• 


• 


• 


• 


• 


• 


t 


• 


• 


• 


• 


• 


•a 


r- 


K Z 


« 




0B 


CO CD CO 


f- 


CM 


•-< 


IT 


r- 


«»■ 


n 


CO 


CM 


CM 


f-4 


UJ 


»m 


< < 
















•-4 


^H 




















O 


ml 




































u. 


o 


UJ to 




































O 


-J 


a. to 






f»> 


—> 


o o 


•O C" 


--* 


•c 


* 


m 


CO 


P- 


-H 


o 




UJ 


< 






o r- 


cc 


00 


o> 


4- 


^^ 


o- 


r- 


* 


m 


p- 


co 


--• 


00 


> 


> 


X X 




o 


■a 


a 


■* 


f-4 


* 


o 


O 


co 


^- CM 


cc 


cr 


o 


CM 


ro 


r- 




3 


o 


■a 


41 


in 


>♦■ o> f- 


ao •» 


■r 


•O CO 


00 


O 


on 


in 


O 


IM 


a 


X 


z 


a. 


CM 


CM 


CM t-l 


CO 


o 


00 


CD 


-H 


«»■ 


sO 


>«■ 


uo 


p-« 


CM 


o 


z 


** 




o 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


t 


o 


3 


X 






00 


ao 


oo 


00 


r^ 


^ 


CM 


o 


00 >f 


CO 


CO, 


CM 


CM 


rH 


-J 


U 


2 


to 


• 














t— l 


•-* 
















UJ 

> 
t 
m4 


a 
O 

1 

CM 




</) o 






































< 


z 


rt 


CM 


c*v -<■ 


—* 


CM 


CO, 


><• m 


p-i 


rM 


CO 


4 


m 


UJ 


UJ 




X 


































to 

•a 
o 


to 

-3 

o 




• 


UJ 






































Or O 






































UJ 


z 


p4 










CM 










CO 
















ae 


< 






































IL 


ec 





































120 



o 

CVJ 
CO 
<L> 

CO 



<u 



o 




Ql 




E 




O 




(_> 




CO 




1 




•1 


I 


o 


o 


«d- 


• 


cn 




1 — 


II 


A 


c 


OJ 


ca 


^ 




03 




3 


• 


CX 


c: 


.c 


O 


+-> 


• r— 


S- 


+-> 


n3 


3 


LU 


i 




o 


O 


oo 


S_ 




+-> 


c 


c 


o 


CD 


•1 — 


O 


4-> 




rO 


r— 


s- 


LlI 


en 




O) 


o 


+-> 


+-> 


rz 




>— 1 


s: 




US 


+-> 




o 


E 


<u 


d) 


S- 


+J 


•1 — 


CO Q 


>> 




CO 







CJ 






CM 


CM CM CM ■£) ~* 


•* o> 


co 


co 


<o 


_■ 


CM 


h- 


o 


•* 






•■■1 








-* CO -* C 0> 


<r 


•—I 


CM 


ao 4 


co 


IT 


r"i m 


ru 






5 1 


a 




LU 


en P- eg a r- 


p- 


CO 


CM 


--i 


,M 


r-4 


o o o o 






»— • 




on 


•# #-• i-i o o 


o 


o 


O 


O O 


o 


o 


O O o 






< 


K 




< 


o o o o o 


o o 


o 


o 


o 


o 


O 


O 


O 






or 


< 




o 


• • • • • 


• 


• 


• 


• 


• 


t 


• 


• 


t 


• 






o 

>- 

X 


a 






o o o o o 


o 


o 


o 


o 


o 


o 


o 


o 


O 


o 






C5 


































Z 






























on 


cc 


•— • 




#-*• 


IT ■-■ LT CM -C 


■* 


cm 


-1- 


ro 


u- 


CO 


■c 


-c 


LT 


«0 




LU 


«o 


0. 






•«* CM P- P- P- 


fM 


cr 


V* 


CO 


CM 


,-* 


-c 


•—I 


a 


r- 




•— 


UJ 


I 




LU 


O a> m J- co 


c\J 


sr 


co 


cm 


<M 


•» 


■—I 


*-* 


o o 




t- 


z 


•a 




OO 


CM O O © O 


pal 


o 


O 


o 


o 


o 


O 


o 


o 


o 




a 


1— 


O 




< 


o o o o o 


o 


o 


o 


o 


o 


c 


c 


o 


o 


o 




LU 


_l 






o 


• • • t • 


• 


• 


• 


• 


• 


• 


• 


t 


• 


• 




a 










o o o o o 


o 


o 


o 


o 


o 


c 


o 


o 


o 


o 




o 


































CC 


































a 








































• 


—■ 


c niMNir 


m 


in 


pw] 


CT- 


CO 


•4 


4 


pal 


cc 


f. 




_ 






O on 


*NfllOO 


o 


a 


ao 


CT 


«0 


m 


Jj 


^ 


m 


r- 




< 






LU 


a. 


m co ■-• p- r- 


p~ 


•4 


CD 


a 


•—• 


«— t 


r- 


»-* 


f 


•* 




o 






a. 


i_> 


^ — i *c cr <r 


4 


.—1 


r- 


.0 


* 


o 


e i 


»1 


o 


tr- 




o 






LU 


—- 


O —•-*—< 00 


cm 


-c 


co 


o 


po 


in 


r- 


m 


IT 


vt 




z 










• • • • • 


• 


* 


• 


t 


• 


• 


• 


• 


• 


• 


UJ 












o o o o o 


o o o 


•- 


- , 


p* 


c- 


IT. 


vO 


a> 


(X 

o 


































































LU 








LU 


• 
































Q 


c 
























o 








o 


z 


~< cm co j- in 


*-4 


CM 


f 


<t 


If 


f— « 


p 


rr\ 


-» 


ir> 


< 








ar 


























a 
D 



CO 



CD 
CO 

c 
o 

Q- 
co 
cu 
a: 





«». 


or 


p- 


LT, 


-o 


p- 


CO 


p- 


cr 


a 


P- vt 


<»■ 


p> 


IT. 


CM 


p- 








(\j 


O 


•*• 


4 


•* 


(M 


p- 


co 


>-4 


p- 


in co 


p- 


p> 


c 


m 


IT. 


LU 










<M 


CO 


a 


a 


f—t 


o- 


P- 


in 


4 PvJ 


o> 


f^ 


in 


c\, 


r-r 


"vl 






LU 


—i 


CO 


IM 


a 


o 


•-* 


<o 


(N 


(V 


ry «J- 


c\; 


(SJ 


r-< 


<H 


ff 


tm4 






tn 


< 


CO 


cr 


0- 


IT 


o 


o 


O 


o 


o o 


•— • 


»■-♦ 


•- 


»— < 


c 


a. 






< 


D 


• 


t 


• 


• 


• 


1 


• 


• 


• • 












< 






«_) 


►- 


o 


o 


o o 


o 


(-4 


*-t 


ri 


w~t »-l 












LLI 








o 






























z 








< 






























_l 




LU 




o 






























D 




o 


•v 


<r 


p-1 


~o 


CO 


r— i 


4 


>o 


o 


fSJ 


p- -- 


r<- 


~-* 


IT! 


00 


CO 


»- 




<•) 


— ( 


at 


t-4 


r«4 


>o 


-»• 


CO 


fM 


o 


io 


p- CVJ 


p- 


O 


O- 


ICN 


if 






Z Z 




Q 


r- 


co 


cr 


■£ 


-0 


p- 


a- 


P- 


>0 ^ 


•4- 


(M 


~C 


p- 


p- 


O 




o c 


LU 




•— . 


rr 


a- 


0- 


V 


^-1 


o 


o 


o o 


W-4 


--* 


O 


o 


o 


LU 




lO •- 


«/1 


-J 


O 


O 


o- 


cr 


o- 


o o 


o 


o o 


O O O O 0* 


lO 




•- »- 


4 


< 


t 


• 


• 


• 


• 


• 


• 


• 


• • 


• 


• 


• 


• 


t 


3 




ce r> 


UJ 


3 


~H 


^H 


o 


o 


o 


■-* 


^-* 


r-* 


•-< w-< 


w* 


^_, 


,— . 


^-1 


o 






<I _l 




h- 






























on 




Q- O 




<_) 






























•M 




Z oo 




•I 


































o 


































-^ 




o 


«v 
































z 






O 




O 


C 


a- 


r- 


CO 


ir 


u - . 


IT- 


p- p- 


Cm 


* 


r— ' 


(N, 


■* 


LU 






< 


CS 


P- 


m 


a 


-* 


>» 


a 


cr 


ar 


c\i c 


cr 


■0 


<r 


LO 


00 


_l 






cu 


< 


o 


-0 


IT 


o 


^^ 


CO 


,— » 


rj 


CSJ p- 


<T 


c 


(T 


O 


cr 


oc 


LU 




Q 


CC 


<o 


-c 


o- 


p- 


rg 


4 


-t 


-r 


•O CO 


r«1 


vj 


4 


in 


<£ 


c 


o 






D 


ao 


CO 


a 


o- 


a 


cc 


a 


a 


co cc 


cc 


CO 


CC 


a 


ao 


o 


or 




_l 




• 


• 


# 


• 


• 


• 


• 


* 


• • 


• 


• 


• 


• 


i 


0. 


c 




< 


O 


o 


o 


o 


o 


o 


o 


o 


o 


o o 


o 


o 


o 


c 


O 




LU 




3 


z 






























C5 






t- 
































<I 


cr 



































< 


uu 








CM 


^-* 


CC 


p- 


in 


r~ cm 


•0 


in 


u 


p,i 


CO 


— PI 


•D 


3 


X 






CM 


0- 


P- 


p-l 


ro 


in 


•* *> 


IT. 


m 


w-4 


o 


r?> 


p- p-l 


F-l 


(- 


»- 


z 






CI 


a 


o 


cr 


CM 


P- ^. 


CM 


p- 


■40 


an 


oj 


p" cr 


CO 


o 




LU 




UJ 


IT 


ro 


m 


>o 


P- 


a ■>» 


o 


l*i 


If. 


CO 


tfi 


<T if 


<o 


«j 


UJ 


LU 


C5 


on 


4 


in 


ro 


CM 


^i 


4- CM 


ro 


p> 


P- 


ro 


P- 


ao in 


in 




»SJ 


2 


4 


«I 


• 


• 


t 


• 


• 


• • 


• 


• 


• 


• 


• 


• • 


• 


z 


t— i 


t- 


OC 


O 


P- 


CO 


co 


CO 


O- 


*> in 


rn 


r> 


4 


•o 


in 


•4- CO 


a_4 


|M| 


a. 


UJ 


a 




,-t 










~-< »-• 


_^ 
















< 


cc 
































o 


LU 


^» 


oc 






























LU 


z 


t- <s> 


< 




CM 


in 


•—i 


cc 


o 


00 O 


P- 


CM 


•» 


oo 


pj 


-< <C 


P- 


r- 


t— 


Z UJ 


LU 


t-H 


CM 


P- 


CM 


CO 


<r, 


•-• <o 


m 


cr 


CM 


« 


u\ 


CO _l 


CM 


^ 


mj 


UJ X 


z 




P- 


00 


CM O 


CO 


O p- 


in 


pg 


>C 


p> 


<» 


cr ^ 


ro 


0. 




z «_> 


1-^ 


UJ 


,-t 


>»- 


f^ 


o 


CM 


00 p- 


•c 


O 


O 


m 


^ 


•-4 CM 


n 


X 


o 


LU Z 


-J 


on 


W-* 


in 


m 


m 


U 


>o CP 


O 


<o 


iT\ 


p- 


^-i 


<»■ CM 


•T 


c 


r- 


O "- 




< 


t 


t 


i 


• 


• 


• • 


t 


t 


• 


• 


• 


• • 


• 


(_> 




< — 




O 


o 


cr- 


co 


CO 


o 


m ■♦ m 


p> 


4 


IT 


if 


4- CO 


•— i 


•M* 


o 


_l 






CM 








—< 


•—I ^i 


^^ 
















UJ 


a. u 
































on 


on 


oo z 
































on 


-> 


— 3 






P- 


co 


o 


r-* 


m 


•"■■ >*• 


C 


PJ 


**■ 


O 


<f 


cr o o 


•a 




o o 


-J 




4 


p- 


cr 


u 


o 


o o 


*-* 


00 


P- 


* 


-T 


p- cr 


•0 


z 


V 


a 


< 


o 


ao 


p- 


>»■ 


— 1 


o 


o ro 


CD 


1— t 


o 


>r 


on 


oo a- 


<c 




*— • 


UJ o 


3 « 


P- 


CJ- 


cp 


PI 


o 


CM ■» 


^ 


in 


o 


m 


CO 


co cr 


pp. 


X 




> 


H 


cc 


P- 


9-4 


CP| 


in 


o 


J- ao 


c 


in 


u-\ 


•c 


o 


rr\ —l 


-4 


i_) 


> 


— o 


«_) 


i_l 


t 


• 


• 


t 


• 


t • 


t 


• 


• 


• 


t 


• • 


• 


•u 


r— 


rj- Z 


< 




o> 


o> 


CO 


CO 


o 


m •»• cm 


t^ 


•a- 


m 


in 


4 CO 


•-i 


UJ 


— 


< « 






»H 








f-4 


r-< <-< 


f-l 
















U 


_J 
































LU 


o 


uj on 
































O 


_l 


oc on 






m 


<? 


•—i 


p- 


*•* 


4 o- 


o- 


p^ 


ao 


0* 


<-* 


O 4 


oc 




UJ 


« 






(M 


CM 


O 


o 


CO 


>o ^ o 


O o 


o 


w-4 


0» or 


o-> 


> 


> 


z z 




o 


p- 


P- 


in 


t— 1 


p- 


CPl C 


4 


CO 


t-< 


CM 


P- 


vO m 


f~H 


t— 




r> 


O 


< 


P- 


f-» 


CI cr 


*-t 


•c m 


in 


in 


.* 


CO «» 


•O CO 


m 


1-4 


Q 


z 


z 


oc 


0> 


vO 


m 


p- 


a 


-4 r- 


p- 


c^ 


—4 


p- 


o 


e- p- 


<« 


u 


Z 


^^ 




a 


• 


• 


• 


• 


• 


t • 


» 


# 


* 


• 


• 


• • 


• 


u 


3 


X 






CM 


o 


CO 


00 o 


oo in 


p-\ 


CO 


m 


~C 


<o 


in co 


f-i 


-J 


U 


< 






IM 


—4 






—4 


f-C •-! 


»^ 














LU 


OC 



on O 

< z 

z 



t-i cm co «* in 



•m cm co ^ in 



>-i cm co -4 in 



• UJ 
O O 
UJ Z 
oc <a 

lu or 



121 





+-> 




C 




cu 




c 




o 




Q. 




E 




O 




o 




oo 

■ 




1 




•>LT> 




O O 




<3- • 




t?>- 




1— II 




n CO 




co oa 




jx: 




(O 




Z3 ' 




CX C 




-E O 


r— 


+J -e- 


CM 


i- +-> 


• 


03 3 


CO 


LU i— 




O 


CD 


o oo 


r— 


S- 


jQ 


■M E 


CO 


C O 


1— 


CU T- 




O -M 




rC 




i— S- 




lu en 




cu 




o +-> 




+-> C 




H- 1 




s 




<J3 -l-> 




u 




E CU 




a; s_ 




-l-> •!- 




CO Q 




>> 




00 



cu 

CO 

c 
o 

Q. 
CO 
CU 

a: 







o 






CM 


«M cm «M <c 


<»■ 


•*■ o 


mm* 


f*4 


CM 


r^- 


O *t 










•— 








HIHH 


o- 


<r 


a ~ 


CM 00 4 


m 


in 


m 


e«"^ cm 










_l 


c 




111 


CIMMO 


o 


h- ro 


INI —< — 


,_! 


O 


o 


O o 










r> 


■— 




(/> 


V* 4-4 .H 


o 


c 


O O 


O O o 


o 


o 


o 


o o 










< 


»- 




< 


o o o o 


c 


O O O O O 


o o o 


o o 










a 


«J 




o 


• t • 


• 


• 


• • 


• • • 


f 


• 


• 


• • 










c 


a 






o o o 


o 


o 


o o 


o o o 


o o 


o o 










V 


































I 


z 




























CO 




a; 


I—* 




— t 


*C Cr >C o 


o 


f-H 00 


*• h- en 


CM 


r- 


oo 


<; m 






UJ 




< 


a 






•-" O CM 


ir\ 


r» 


<t r^ 


*c •-> r~ 


* 


o- 


.0 


m «» 






— 




UJ 


X 




LU 


m -O nT en 


CM 


0> m 


CM CM ~* 


CM O O 


o o 






t- 




z 


■a 




l/> 


-» o o o 


O 


o o o o o 


O o 


O 


o o 






a. 




IM 


c 




< 


o o o o o 


o o 


o c o 


o o 


O 


c o 






UJ 




_ 1 






o 


• • t 


t 


• 


• • 


• • • 


• 


• 


• 


• • 






a 












o o o o 


c o 


o o o 


o o 






o 


































a 


































a 










































• 


#■■ 


C> CI CM 


CM 


in 


m m 


<-* o- op 


sa- 


~» 


•-< 


oo en 






-i 








O CO 


>* cm oc 


C 


o 


o o- 


CO c> »o 


in 


vO 


vf 


en e> 






< 








LU 


a 


m en *- 


r- 


r» 


r- vJ- 


oo a r-< 


»•< 


h- 


p~* 


en ^t 






O 








<X 


<_> 


^ ^ <c 


& 


•» 


* — 


r^ o -4 


o 


en 


«* 


o m 






D 








U- 


^* 


o •-• *-* 


—> 


CM 


CM ^5 


00 o c 


in 


r» 


en 


in t-i 






I 












• • * 


• 


• 


• • 


• ft 


• 


• 


1 


• # 


LU 
















o © o 


o 


O 


o o 


o -- ^ 


■"* 


en 


If 


<£ or 


a 

o 


































































u- 












LU 


• 
































o o 




















o 












o z 


.-i CM en 


-» 


in 


—< cv 


if ■} in 


r~* 


e\' 


m 


.* m 


< 












X 


< 




















or 

O 

LU 

I 
1- 












*s. 


or 


Hirf 


o 


00 


~t 


h- >C f- 


.-« 


O 


t- 


en oo 














<M 


o 


aN « 


CD 


W 


O r~- 


h- O ^ 


CM 


•— • 


p-i 


vt a 


lil 
















-«■ o> c 


a 


i— i 


•-I o* 


00 00 en 


in 


in 


in 


m en 


KJ 












UJ 


_i 


a- a a 


0" 


Ci 


CM ■-* 


^ — C 


o 


O 


o 


O -> 


»-i 












OO 


4 


oo o o 


0- 


o> 


o o 


O C O 


o 


O 


o 


O O 


OC 












< 


3 


• • • 


• 


• 


• • 


• • • 


• 


• 


t 


• • 


< 












<_> 


»- 


O O O o 


o 


■M t-l 


»— i ■— i a— ■ 


p— ' 


^i 


*-< 


»■* •— < 


LU 














O 




















Z 














<t 




















-J 




u. 










o 




















o 




o 








^ 


< 


—» m f- 


,_• 


CM 


C«1 >t 


ej> <o o 


r~- 


CM 


in 


o er 


1- 






00 






pal 


or 


r- o> co 


cr 


4 


CM f^ 


r>- a- in 


rr. 


esj 


e\l 


in oo 






z 


Z 








o 


r- o o> 


a- 


00 


in c* 


CM CM O 


■H 


t— * 


f-» 


-4 <o 


o 




o a 






UJ 




O <J> o 


a- 


0> 


f-« f-i 


^ ^-i O 


o O C 


O o 


LU 




co 


»_ 






O0 


-i 


o o> cr 


o- 


C 


o o 


o o o 


O 


O C 


O O 


co 




p— 


t-- 






< 


« 


• • • 


• 


• 


• • 


• • • 


• 


• 


• 


• • 


3 




a: 


r> 






«_) => 


— o o 


o 


o 


















•s 


-i 








t- 




















CO 




a 


o 








u 




















— 




i 


CO 








< 
























a 






























MM 




<_> 








**. 






















X 












o 




•■4 m cm 


m 


o 


<C -D 


vO >0 -' 


cr 


c 


a 


st OC 


111 












< 


o 


en cr o 


O 


in 


C f- 


O en ^ 


en 


NX 


eN_ 


O O 


_J 












or 


•or 


en 0" o 


CT 


vf 


m o> 


Com 


O 


o 


c 


O ao 


CO 


LU 










O or 


— < o o 


O 


m 


^ ^ 


in in oc 


a- 


o- 


o 


ej> f- 


O 


O 












Q 


ff- o- o 


o 


o 


O 1 CT 1 


0" a s 


o- 


cr 


a 


ej- a 


or 


or 










_) 




• t • 


• 


t 


• • 


t • • 


• 


• 


• 


• • 


a 


c 










< O 


o o — 


w~ 


o 


O O 


COO 


o 


o 


o 


O o 




LL 










3 


Z 




















C 












t- 






















<. 


o 










u 






















a 


< 










< 






















o 

-J 


a 

O 

LU 














o> ^ 1*- 


a- 


o 


a m 


>» >C oo 


P4 


<? 


~c 


IM O 


z> 


X 












CM 


O (M<t 


•-* 


en 


-*■ st 


in >f <o 


•* 


r-l 


f-- 


ex en 


H 


K 


z 












-< o o 


•c 


00 


r»- o 


r^ o ^■ 


CM 


in 


o 


cm a 


O 




UJ 










UJ 


(Men H 


o- 


f^ 


•C CM 


en n£) O 


o 


m 


ev 


CM h- 


< 


tu 


UJ 








O co 


i*> CM CM 


o 


^~ 


m o 


cm 0* r~- 


oc 


Nl 


cr 


O ej- 




C-J 


3 








< 


< 


• • • 


• 


• 


• • 


• • • 


• 


• 


• 


• • 


z 


•— 


t- 








(X 


o 


oeec 


oo 


•c 


ff> m 


H«n 


en 


i*i 


esj 


CM O 


•— 


or 


UJ 








D 




p4 






v-i •--< 


p>4 












< 


BE 


^ 






a: 






















o 
u. 


UJ 

z 


1- 


oo 






< 




CM CM -H 


oc 


CM 


o> en 


moH 


oc 


e\j 


to 


en en 


0- 


*•« 


2 


LU 






UJ 


—1 


OHO 


o 


•-* 


O" o- 


in >t ao 


00 


0- 


en 


a >» 


J3 


-J 


UJ 


I 






z 




CM «-t (T\ 


f- 


o 


CM (f- 


#-< in ^ 


r- 


*-* 


tr 


•* CM 


a 




I 


1-1 






•— 


UJ 


CM fr. •-• 


o- 


«»■ 


00 s»- 


f" CM 0' 


00 


CM 


o 


•-• r- 


X 


o 


UJ 


Z 






_J 


CO 


•C CM CM O 


V 


CM O 


~4 0"> >f> 


r- 


>r 


cr 


O cr 


o 


»- 


<_> 


■— 








4* 


• t t 


• 


• 


« t 


t • • 


• 


• 


t 


t • 


u 




< 


<-* 








(_> 


— i <c <r 


0D 


~o 


ro cm 


i-i <o en 


en 


en 


CM 


CM O 


»«p 


o 


-J 












■H 






— < *-* 


•-4 












UJ 


a. o 




























1/) 


I/) 


CO z 




























CO 


_> 


•— ■ 


r> 










humt 


m 


* 


*- •* 


f- O m 


oo 


IT 


en 


O O 


< 




Q U 






-1 




hNO 


OD 


-H 


■C en 


* eoo> 


<o 


f~ 


p- 


cr oo 


X 


1/) 




a 






< 


o 


en CM * 


r^ 


t^ 


en * 


O -O CM 


eM 


e^- 


u^ 


*-* m 




1-4 


UJ 


u> 






z> 


•a 


mcorf 


a- 


in 


oo r^ 


en r , ej> 


oc 


PM| 


c 


-« « 


X 




> 








t- 


a. 


in CM CM 


o 


V 


o r-- 


oa« 


f^ 


vt 


a 


o cr 


<_> 


>■ 


<— 


LJ 






l_> 


LJ 


• 1 • 


• 


t 


t • 


« • t 


• 


I 


• 


• • 


<l 


e— 


*~ 


z 






<l 




riCO 


00 


-c 


en «m 


~* •& en 


en 


en 


evj 


CM O 


LU 


*m 


< 


< 










•-I 






«* f-* 


p4 












O 


_J 






























U- 


o 


UJ 


oo 




























O 


-J 


a 


oo 










r^ o .o 


00 


a 


^ en 


O .-• O- 


•-4 


h- 


en 


11*1 >t 




LU 




< 










»>- f^ 00 


v\ 


* 


CM o 


o a o 


<o 


00 CM 


-l «»■ 


> 


> 


z 


X 








o 


r- cm in 


r~ 


CM 


«* O cm en cj> 


e> 


O 


>T 


CM 1^- 


t- 




D 








o < 


NltH 


c- 


00 


■4 m 


o ey m 


«-« 


in 


en 


<n 00 


•— 


o 


a: 








z a 


O CM CM 


o 


CM 


00 -* 


<0 ^h r>- 


00 


-t 


e> o ej> 


u 


z 


■— 










D 


• • • 


• 


• 


t • 


t • • 


• 


• 


• 


• • 


o 


o 


X 












CM 00 00 


00 


r- 


ir en 


t-< f- c- 


en 


r<^ 


esj 


CM O 


-J 


o 


«J 












r-> 






—* *— < 


«-^ 










LU 


or 


x 








CO 

co 


• 




















> 
1 

•-4 


o 
1 

CM 










< z 


~* CM CI 


sf 


m 


-< cm en 


•-4 


cm en 


LU 


LU 










X 






















CO 

< 


co 

< 



• LU 
O O 



or « 
u- ec 



122 



U CM 

-JO UJ 

D — CO 

< t- < 
or < o 

a 
V 

1 O 

z 
a — »* 

< a. 



»- z « 
a .- c 

U- -J 

a 
o 
ac 

a. 



co 

< 



o 
o 



u-i a 
or. o 
u_ — 





E 




ai 




c 




o 




Q. 




E 




O 




c_> 




00 

1 




1 




•n •— 




o o 




«3- • 




<Ti 




i— II 




« to 




a> ca 




.*: 




rO 




13 • 




O" e 




-e o 


C\J 


•»-> T- 


OJ 


i- 4-> 


• 


rO 3 


CO 


bJ i — 




O 


a; 


O 00 


r— 


S- 


_Q 


+-> e 


rO 


e o 


I— 


ai ••- 




O 4-> 




<T5 




i— s- 




lu cn 




0) 




o -t-> 




+-> E 




i— i 




nr 




<£> +J 




O 




E <U 




OJ S- 




+-> •■- 




oo O 




>> 




oo 





o o 




o z 




X 




o 




< 




«v ac 




Pg O 




Ui -1 




CO < 




< z> 




o P- 




o 




<• 


LL 


o 


O 


V < 


co 


— ' a 


z z 


o 


o o 


UJ 


CO *- 


CO _i 


1— C- 


< < 


a: D 


O D 


< _j 


K- 


a o 


O 


z to 


< 


O 




o 


n» 




o 




< o 




CC < 




O CC 




o 




_l 




< o 




=3 Z 




»- 




u 




< 



<u 

CO 

E 

o 

Q. 
CO 
<D 



o •- 

< — 

a. a 
to z 

<- Z) 

u u 

cc 

> 

— CJ 

•- z 

< « 
_j 

ai to 
a to 
« 
Z Z 
3 



X 
< 



< «t 
O 



to 

< 



t- ac 



o 
o < 
Z ac 

o 



CO • 

CO o 

< z 



• UJ 

a o 



ac « 
u. ac 



in «r urt —I ao 

go * * a> in 

<om(MH « 

o o o o o 

• • t • • 

o o o o o 



m to go m a> 
o *m 4> p- cp 

Mnoo« 

PhhOO 

o o o o o 

• • • • • 

o o o o o 



cp n pg pg ir\ 

^NCOO 

in ro i— r^ p- 

«t f^ *o ^ -^ 

O -- ^ *-l <M 

• • ♦ • • 

o o o o o 



— pg m >4 in 



If* CO IM go 0D 

m ** ft P"» CP 

O fr ^ >* (*> 

p» o cp cp •*> 

P- CP CP CP ao 
• • • • • 

o o o o o 



cm a> r- p- rvj 

od i-c lt r- j 

gO O CP J} go 

eg un CP cp CP 

O O ff> a> Cf 

• • • • • 

— I r* O O O 



oo o a- %o <m 

ro ir> <r in o 

*o ao o -^ vO 

r- r- t> o> oo 

• • • • t 

o o o o o 



o o — cn o 

C O h4 (»* 

rri oc r- -C (M 

M «M fv %0 ro 

in m o eg as 

• • • t • 

fO 00 00 0D r- 



crir ib 4 O 
u - ' go ao oo O^ 

im (f* ro o ir\ 

O r» «*< <M ft 

t • t • • 

oo oo ao or cj* 



0> r>- wa <• in 

a n 4 n ir\ 
uo^iiiM 
ininoipiff' 

# • • • • 

r* oo oo eo cr 



fn o ^i f-- — < 
NNOOCI 

•*■ r- m -* t>- 

p~ -* f\ & *+ 

v <o (ti r- o> 

• • • » • 

N O CO CD O 

(M —> t-t 



— cm ro ■* tft 



00 OO * f- (M 

1 r, 4 o a- 

<f> <0 •* f" <M 

•-•OOOO 

OOOOO 

t • • • • 

OOOOO 



C ^-1 4- r>j & 
—> <r <nj —> o 
<nj ao * in ■* 

NOOOO 

0000c 

• • • • • 

OOOOO 



IT U"i —1 O" QC 

O f/ CO 9 <£ 

r- ^ 00 o —1 

«*• #-. r- -o «j> 

P<0 >0 00 O C> 

t t • • • 

o o o •-• -< 



hm it ^ ui 



o »^ m m o 

NCITi IT •-> 

o> 00 r- r-- a 

m «* >f <sj eg 

00000 



P- O 0> r^ m 

CT* CP <*** IT\ CP 

»© •-* O t-H ^^ 

<V fSi <NJ O t> 

ooooo- 

• • • • • 

_ -, -, _- o 



•* »< ro <P in 
iv. <0 •-• ro <t 

o> cp cp ro r^ 

t^ cc ao ao oc 

• • • • • 

OOOOO 



OOIT44 

t— r^ m <p ■* 
O rr> oc o m 

IMIfl«0>i- 

• • • • • 

in <*■ rg p- «»• 



oo <* «-i CP >o 
4) rg p- if. <C 

MH -( ^U1 

m p- m o m 

siciiMnM 

• • • • • 

•* «»• pg p- ■♦ 



f^ ^-1 ^- o *+ 

m *-l eg t-t f\j 

NP*00 

*> go 00 cp cp 

40NWN 
• •tat 

•* •♦ eg P- <■ 



•* CP CP f» 00 

«400m 
o o> <cp 00 >H 
■o m m m ■*• 



co if n « if. 



•— pg m ■* m 



Hinmoco 

<0 O P- «3 <f 
Pg «h o O O 
OOOOO 
OOOOO 
t t t • * 
OOOOO 



cd r^ oc O go 

p- pg eg »-i t-4 
OOOOO 
OOOOO 
t • • • • 
OOOOO 



4 — <v 







in go ^ r*\ 


p- 




rfpHfH 


.* 




m 4 O 


m 




m P- f, it 


•-t 




• • t • 


• 


u> 


nmif « 


OC' 


O 
oc 



li- 


rt(\jm< 


m 


< 



oc o O pg pg 

go o pg O r> 

pg O cp «* —> 

•- o f~ go pg 

pg po w-) —> «-« 



IflCP + P 4 

Pg st CM 00 P- 

pg m p- gp ro 

pg —1 O cp oo 

o o O cp CP 

• • • • • 

rt ~4 --. O O 



m if , cp «t f> 

CO %C f. i-i CP 
rr, c in •- O 
4Bi<ajH 
p- p- r~ p- oc 
• • • • • 

OOOOO 



00 p- If . 4 o 

4 O m O- CO 

(M p- fi go <-" 

p- «t <o CP o 

o «t go m m 

• • • • • 

go m 4 fO i-4 



rg CP CP —> m 

s 4NC1IP 

OC CP C* P, P- 

rtOdOri 

h gj o> o ^ 

• • • • • 

m ^- fr> rg -- 



0<T COBh 
mrgg;iMm 

p- cp <• oo cp 

cj m ir »-i m 

o m cp cp m 

• t t t • 



CP »g o gp «o 
o -< cp cp in 

rg p- gj in rt 

po gp <c o in 

r- o — p- go 

t t t t t 

<0g)IP ir<H 



rH pg p-> gp m 



1 
t- 

cu 



o 

UJ 



< UJ 

3 I 

t- t- 
o 

< LU 
Kl 

z — 

►- oc 

< 

O LL 

tu z 

I- — 

Z> -1 

a. 

z o 

O 1- 

u 

~ u 



00 

CO 

< 



X 



CO 



U 

u. o 

o -J 



— O 

u z 

O 3 

_J o 

in ac 

> o 

1 I 

-* pg 



CO 

to 





o 






(VI 


KMnlTMB 


CD CD <c r- (VI 




to* 








NON9 > 


co m *r *j cr 




-1 o 




UJ 


<e -t ■+ <r m 


in <C «t (*t (VI 




=> 


to* 




to 


«OmNr.-l 


•-I o o o o 




4 


t- 




< 


o o o o o 


o o o o o 




a. 


< 




U 


• • t • • 


t • t • • 




o a 






o o o o o 


o o o o o 




X 


z 










«/> 


a 


to- 




t-t 


*o <*><«• a m 


•o r- (vi (vi o* 


tu 


< 


Q. 






o* <o »* *0 C*l 


CD •■* O to* (VI 


to- • 


tu 


X 




UJ 


<o i-< to <c irt 


r- r- m ^- i*i 


t- 


Z 


< 




IO 


(M -* O O O 


— o o o o 


ct 


to* 


c 




< 


o o o o o 


o o o o c 


UJ 


-J 






u 


t • • t • 


t • • t • 


Q. 










o o o o o 


o o o o o 


o 














cc 














a 




















• 


toto 


o» »*i cvi (vi in 


in in to* o- ec 


-i 






O i/> 


<t IMCDOO 


o cr op cr *o 


< 






UJ 


a 


m fn to* r- r- 


to- ^ od a to- 


o 






ac 


«_> 


<H«J.+ 


<*• to. r- 4) «<• 


o 






li. 


«» 


O f-> to* i-t <M 


(vj <o oc O i*> 



to* <r m o ac 

•c o r^ ** <•■ 

(VI to* © o o 

o o o o o 

o o o o o 

• • • • • 

o o o o o 



i*i o (*» a f~ 

f- 0* <*i o on 

«1* to* to* to* O 

o c o o o 

o o o o o 

t • t t t 

o o o o o 



123 



e 
a; 
e 
o 

Q- 
E 
O 
C_> 



Q O 

O Z 

x 



o o o o o 



■■* (VI <*> «» m 



O O O to* -* 



J*-' 


00 1*1 




ir *3 <» 


i*i r- 




r* to- to4 


(*• •* 




O <*! ■* 


O in 




IT> f" (*l 


in to* 




• • t 


• • 


UJ 


to* 1** UV 


*; od 


O 

or 
o 
u. 

o 


•-* <M (*1 


.*- in 


< 
or 

o 



00 





"un 




o o 




>=*- • 




cr> 




r— ii 




•« cO 




co ca 




_^ 




(O 




3 • 




ex e 




-E O 


oo 


■»-> »r- 


CM 


S- +-> 


• 


fO 3 


CO 


UJ r— 




o 


CO 


o oo 


1— 


S- 


-Q 


•»-> E 


m 


E O 


\— 


OJ •!- 




O +-> 




(O 




i— i- 




UJ CD 




OJ 




o +-> 




+-> E 




i— i 




DC 




vO *-> 




a 




E CU 




a> s- 




4-> ••- 




CO Q 




>> 




CO 



QJ 
(/) 

E 
O 

a. 

CO 

CO 

a: 







•v or 


o» v\ ao 


*3 (*) 


«*t 


m 1*1 


o> o 


o> 


■^ to* r- *3 










<M O 


(*»«<•■* >o 


co 


ao 


to* -* 


(*i 


IP* 


to* 


a o *3 >t 


UJ 










CO O* 0* 


o 


(M 


o 


in «»• 


in 


(*1 


o 


a o o «o 


KJ 








UJ _l 


-o a o 


o 


r- 


(M 


»*i «*i 


r*\ 


o 


to*] 


O to* to* (vi 


to* 








to < 


00 O s 


o- 


c 


O 


o o 


O 


o 


o 


o o o o 


a. 








«* D 


• t • 


• 


• 


• 


• # 


• 


• 


• 


• • • • 


< 








o •- 


o o o 


o 


o 


■-* 


to* to* 


r-i 


to* 


_4 


■-* ■-* to* f-* 


UJ 








o 




















z 








< 




















-1 




u. 




o 




















o 




a 




■V < 


•MOO 


to* 


1*1 


<o CO 


ac 


r- 


to* 


o>c»((i<t 


r- 






IO 


to* or 


pj r- oo 


CD 


ao 


to* 


o o> 


^* 


m 


a 


m m ivj oo 






z z 


a 


to* o o 


a 


h- 


(M 


•O u" 


K 


cr 


(V) 


(VI (VI (*l (VJ 


Q 




o o 


ill 


-«1 c> o> 


a 


o> 


fmt 


(VI (VI 


«VJ 


a 


o 


o o o -* 


UJ 




to 


to* 


to -J 


o»t> 


a 


e> 


c 


o o 


o 


a 


o 


o o o o 


to 




to* 


to- 


< < 


• • • 


t 


• 


I 


• • 


• 


t 


• 


• • • • 


3 




a 


3 


O 3 


•-* o o o 


o 


to* 


to* to* 


to* 


o 


to* 


•-I #-* •-* »h 






< 


_J 


K 




















IO 




a 


o 


u 




















to* 




X 


IO 


< 
























□ 
























to* 




o 




>> 




















X 








19 


to* o o r» 


o 


*0 


■O f^ 


*0 


o 


<» 


ff"< cm 


UJ 








< O 


«*i o o 


o 


o 


o 


(*1 IM 


a 


IT 


o 


to* o d (VI 


-1 








or < 


r- o o o 


in 


«t 


■O fto 


u- 


CO 


to* 


to* to* O ac 


CO 


UJ 






o or 


^ o o o 


to* 


p* 


o o 


O 


o 


ao 


CC OD 00 IT 


o 


o 






o 


eo O O 


© 


o 


o- 


cr o> 


a 


a> 


o< 


0> ff CfO" 


ar 


or 






_i 


• t • 


■ 


• 


• 


• • 


• 


t 


• 


• • • • 


a. 


a 






< o 


O •-) •*> 


•-* 


o 


o o 


o o 


o o o o o 




u. 






3 z 




















o 








►- 




















< 


o 






(J 




















or 


< 






< 




















a 

-1 
< 


ar 

Q 

UJ 








•»l>c» 


r- 


(M 


to* 


<M to* 


<vj >o 


r- 


(*! to* *D ^ , 


3 


X 






fSJ 


<4- to* ITi 


c-i 


•t 


o 


«-* (VI 


o 


a- 


i*i 


*D •* U"> <M 


K- 


1- 


z 






-*) eo -* 


in 


a> 


00 


O O 


OD 


to* 


m 


0» r- fri ,* 


o 




UJ 




UJ 


0* CM to-t 


a 


oo 


*-* 


to* CO 


•*■ 


m 


00 


to* o to* r- 


< 


LU 


UJ 




cj to 


r\j eo im 


O 


«1- 


0> 


•O CO 


r- 


«o 


r- 


** o o o> 




to* 


X 




< < 


• • • 


• 


• 


• 


• • 


• 


• 


• 


# • • • 


z 


to* 


to- 




ar o 


s 00 00 


oo 


o 


(M 


(Vi O 


-o 


m 


Cl 


(*i (VI rvi o 


to* 


or 


UJ 




Q 








to* 


to* to* 












« 


CO 


«. 


or 




















a 

UJ 


UJ 

z 


t- 


to 


< 


<*• fsi tn 


<* 


(M 


(M 


*j ao 


o 


o 


o 


vi- >r in *D 


r- 


to* 


z 


UJ 


UJ to* 


r- o (v. 


o 


(M 


(*t 


m (vi 


u< 


to* 


to* 


r- o r- (*, 


3 


-J 


UJ 


X 


z 


a -* >»■ 


o 


<o 


CD 


cr O 


•* 


o> 


ac 


-» -O HOC 


a 




X 


u 


to* UJ 


•I m «-i 


a 


m 


o 


to* O 


O- (*l 


in 


cr oo cr m 


X 


o 


tu z 


-j to 


00 (M (M 


o 


•c 


00 


in ao 


<o 


•e 


p- 


(*l CD O O" 


o 


t- 


o 


to* 


« 


• t • 


• 


t 


• 


• ■ 


• 


# 


• 


t l • l 


u 




< 


w 


u 


O CO OD 


CD 


<o 


(M 


(VI o 


*3 (*i 


m 


(*i (vi •-* o 


Mtoi 


o 


-J 






to* 






to* 


to* to* 












UJ 


a. u 






















to 


«o 


«o z 






















IO 


_) 


to* 


=> 




*r to* o 


\f\ 


<y 


in 


to* to* 


r- 


r- 


o 


<0 ao o "* 


< 




u u 


_l 


*j to- a 


■-* 


<o 


$ 


-o V 


(*i 


*3 


(VI 0* in (*i rvi 


X 


(O 




ac 


< o 


a> cm in 


0D 


o 


o « 


r- o 


p» 


in oo rvi <o 




to* 


UJ 


o 


3 *« 


a (*i ** 


(T 


r» 


IT. 


O (M 


•-* 


«r 


* 


oo r- cr -r 


X 




> 




»- or 


*D (M (M 


O 


<o 


o 


«-< m 


in 


<*> 


r- 


rr, uj cr cr 


o 


> 


•-* 


u 


(_> u> 


• • • 


• 


• 


• 


• t 


• 


t 


# 


t • • • 


4 


to- 


f- 


Z 


•c 


O CD 00 


00 


o 


(M 


(VI o 


•o 


(*t 


e> 


(*l (VI to* o 


UJ 


to* 


*» 


< 




to* 






to* 


to* to* 












u 


-J 
























u. 


o 


UJ t/» 






















o 


-1 


ac «/> 




r- o <c co 


a 


•♦ 


(*i o 


•-* 


a> 


to* 


^ 1*1 m ^■ 




UJ 




< 




r- t» ao 


u-> 


>t 


(SJ 


o 0» 


a 


o 


«0 


CO <VJ -* .*- 


>■ 


> 


X 


X 


O 


r* (N4 U\ h- 


(M 


«*• O IN 


m 


a 


a 


o «*• (vi r- 


1- 




3 




o •» 


(M (*l to* 


O 


00 


* m o 


c 


m 


•*4 


m f (*i oo 


to* 


o 


X 




z or 


O <M M O 


IM 


00 4- <o 


•-* 


r- 


00 


-I JOlf 


u 


z 


to* 




a 


• • • 


• 


• 


# 


• t 


• 


• 


t 


• t • • 


o 


3 


X 






(M 00 00 00 


fto 


«*i 


1*1 »* 


c- 


(*i 


1*1 


(*! (VI cvl O 


_J 


o 


< 






to* 






to* 


to* to* 










UJ 


ar 


X 




io • 

</> o 




















> 
1 

to* 


o 
1 

(VI 






< z 


to* (\J (*1 


•4- 


m 


to* 


cm m ^ 


to* 


(vi (*i *t m 


UJ 


UJ 






X 




















IO 

< 


to 

< 
O 






t UJ 




























o o 




























uj z 


to* 






(M 








(*l 












ar < 




























u. ar 

























124 





u 


N 


0(^«»* 


<• r» inj r» ci 


-OI<i<lff 




Wl 




Mr « ff f 


C O O in —• 


CI m Cl CM t-l 




-1 o 


UJ 


in •-• * O i"» 


r- ci cm ,-< .-i 


— o o o o 




3 ~ 


«/) 


inNHoiO 


o o o o o 


o o o o o 




< 1- 


« 


o o o o © 


O O O O O 


o o o o o 




a «* 


U 


• t • • t 


• • • • • 


• t • • • 




at 
>■ 

1 o 

z 




O O O O O 


o o o o o 


o o o o o 












lO 


ec •- 


«-4 


,o cr r- r- o 


oo ci m c- .-i 


cr >0 0* U"\ <-h 


UJ 


•fl 0. 




m h- * M)- m 


cr va o o r- 


MO O 03 * 


•■4 


UJ I 


UJ 


^ >« «»• W fvj 


«-* * C> CVJ t-l 


-j/ — —i o o 


»- 


Z <J 


t/i 


<-< o o o o 


-« O O O O 


o o o o o 


a 


- c 


< 


o o o o o 


o o o o o 


o o o o o 


OJ 


-J 


u 


• • • • • 


• t • t t 


• • • t • 


a 
O 
a. 

a 






o o o o o 


o o o o o 


o o o o o 




• *•» 


cm ■-! o> cm m 


in mj c* -* cj 


■* cr oc md r- 


-I 




O to 


«\J •-! m> * o 


o .-< -j- ms o 


in C- <C «»■ CM 


< 




UJ & 


tr —i oo co r- 


h- o> t-* •-* •»» 


-* <)■ Mf c- ci 


O 




ec t_> 


ci cr c» c* ^>- 


<f ci r- it. o 


O OD O O CV 


C 




u- — 


O Ohhim 


cm mj o- cm r- 


in oo cr mj in 






O 



O 



1/0 



o o o o o 



o o o •-« •-< 



i-i CI IT t* O 





o o 




"3- . 




CT> 




r— II 




m (/) 




rjj oa 




-s«£ 




rO 




3 • 




cr c 




-c: o 


*d- 


+■> 1- 


C\J 


s- +-> 


• 


ra 3 


CO 


UJ i — 




O 


0) 


o oo 


^~ 


s- 


-O 


+-> c 


fC 


£Z O 


I— 


<]J -r- 




<_> +-> 




f0 




r— S- 




UJ CD 




a; 




o +-> 




+-> c 




•— i 




s: 




r^ +-> 




<_> 




E a> 




<u s- 




+j -i- 




L0 Q 




>> 




00 



to 

c 
o 
a. 
to 
ai 
en 





Q O 


























13 






O 


z 


p4 


rv 


Cl •*■ 


«-< »\i 


c 


-» 


m 


i-i CM 


m 


<t 


m 


<. 






X 


< 


























a. 
a 

UJ 

I 

r- 






N» 


or 


c» 


r<-i 


o 


00 Cl 


r- <J> 


o 


o 


in 


•e ci cr 


>t 


o 








fsi O 


«M 


O 


*(OC 


O ao 


a 


or 


«-4 


w-l Cl 


o 


Cm 


00 


LU 










<0 


(N 


a 


a o 


i-i o- 


vO 


in 


ao 


r- r- 


ac 


00 


<0 


rj 






UJ 


-j 


CI 


0D 


o- 


a o> 


Cl <NJ 


fM 


CM 


O 


ci m 


c 


1-1 


— 


*-* 






to 


<r 


0> 


o< 


a 


c o- 


o o 


o 


O 


O 










OC 






< 


3 


• 


• 


# 


• • 


• • 


• 


• 


• 










< 






o »- 


o 


o o 


•-* ^-4 


-j 


•-I 


—^ 


— * f-i 


w* 


1-1 


rmi 


UJ 








<_> 


























z 








< 


























_l 




u. 




O 


























o 




o 


«». 


< 


M 


00 


Cl 


fVJ t\J 


m r- 


00 


<f 


in 


m ^> 


M3 


in 


00 


K- 




to 


p4 


ec 


CI 


r- 


a: 


00 O" 


ao ao 


o4 cm r- 


cr p- O cm mt 






z z 




o 


<0 


m 


o 


o> 0> 


<V _H 


O 


CT 


cr 


>»■ •<• 


M)- r- 


r- 


a 




o c 


UJ 




o o 


cr 


Ch o> 


i-« i-l 


i-i 


O 


cr 


•-< i-i 


^-> 


o 


o 


UJ 




to *- 


to 


_j 


o o 


o 


t> 0" 


o o 


o 


O 


cr 


o o 


O O 


o 


to 




»- »- 


< 


« 


• 


• 


• 


• • 


• • 


• 


• 


• 


• • 


• 


§ 


• 


3 




a 3 


o 


3 


■H 


f-* 


o 


o o 


•-4 »-J 


*-» 


•-* 


o 


•-I 1-1 


•-» 


r-« 


1—1 






< _j 




»- 


























IS1 




a. c 




U 


























1—1 




X to 




< 






























O 






























*^ 




u 


»%. 




























X 






o 




00 


-o 


o 


00 4 


cr f\j 


o 


CO 


<<• 


r» o 


M5 


•-« 


in 


UJ 






< 


o 


0> 


u^ 


o 


O <V 


Cm r- 


r- 


© 


in 


O OD 


r- 


r- 


* 


_J 






or 


< 


<y 


tr\ 


^ 


o o 


•£ r~ 


rvi 


>*■ 


in 


^)- fn 


<NJ 


w~i 


Cl 


00 


UJ 




O a 


u\ 


~D 


in 


o o 


Cl Cl 


>t 


<}■ 


r~ 


Cl ftl 


Cl 


in 


m 


o 


o 






o 


<? 


a 


a 


o o 


cr cr 


cr 


o- 


cr 


ao oc 


00 


co 


oo 


or 


or 




_i 




• 


• 


• 


• • 


t • 


• 


t 


• 


• • 


• 


t 


• 


a. 


o 




< 


c 


o 


o 


o 


~i w* 


o o 


o 


o 


o 


o o 


o 


o 


o 




u. 




3 Z 


























o 






K 




























< 


u 




(_> 




























or 


< 




< 




























o 

_j 
< 


or 

o 

u. 








Cl 


o 


sr 


C 00 


•o ao 


■H 


1—1 


•o 


r- ^ 


-3" 


r» 


Cl 


3 


X 






CJ 


t- 


-o 


a 


tn •-. 


cr oc 


>1 


O 


CM 


cr Mr 


CJ 


a 


•O 


r- 


r- 


z 






00 


>0 


si" 


<\j k 


cr -< 


cr 


in 


ao 


MS — 


— i 


<s 


Cl 


U 




UJ 




UJ 


-0 


(^ 


c 


•-• a- 


oo O 


<NJ 


a 


<a 


cr m 


«*■ r- 


f- 


•a 


UJ 


UJ 


O 


CO 


CI 


r~ 


m 


Cl -t 


r\j O 


PI 


cr 


%» 


cr r- 


o 


co 


1—1 




inj 


J* 


< 


« 


t 


• 


• 


• • 


t • 


1 


# 


t 


• . 


• 


• 


• 


z 


■— 


1- 


K 


o 


o 


oo 


ao 


oo r- 


-O in (\j 


00 


in 


ir m 


in 


r»l 


CM 


i«i 


or 


UJ 


O 




_l 








1-4 «_« 


•— 1 
















•a 


09 






























e 


UJ 


M 


a 




























UJ 


z 


►- to 


< 




in 


r-l 


in 


oo o 


00 o 


in 


•* 


—4 


-* ao 


CO 


•c 


M5 


r- 


■— • 


Z UJ 


UJ 


f-4 


ao 


r\j 


in 


-H O 


O tri 


00 


r- 


r- 


IT. M) 


CO 


•— 1 


CO 


3 


_l 


UJ X 


z 




>♦ 


—^ 


CD 


<C f^ 


<\j cr 


Cr 


u 


M 


CM ^ 


1-1 


CM O 


a 




X <_> 


M 


UJ 


■♦ 


<M 


c 


i-i o- 


O f. 


<M 


IT 


CM 


m ci 


c 


cr 


M3 


X 


o 


uj z 


_l 


to 


f4 


in 


c 


Cl <*• 


o r» 


i—i 


00 


«r 


Cl — 


^ 


«»■ 


a> 


o 


K 


t_> "- 




< 


• 


• 


• 


• • 


• • 


t 


• 


• 


i t 


t 


t 


t 


l_> 




< — 




o 


■-4 


oo 


00 


oo r- 


•c ~t 


Od 


CO 


in 


m m 


Mf Cl 


•-i 


«»■ 


D 


_) 






f-4 








— > — 1 


—* 
















UJ 


Q. £_> 






























to 


to 


to Z 






























l/l 


-J 


— 3 






C«J 


>»• 


m 


K o 


in «»■ 


#— * 


-0 


ao 


in mj- 


M5 


Cl 


O 


< 




U u 


_l 




o> 


#■* 


o- 


«o r- 


o m 


>»" 


>0 


o 


O cr 


m 


O Cl 


3L 


l/> 


or 


< 


o 


■JJ- a> 


a- 


r- r~ 


cr * 


-0 


V 


•* 


Cl -o 


cr 


f- 


<4> 




— 


UJ o 


3 « 


r» 


ao 


Cl 


~4 t7> 


0- « 


o 


•c 


IV 


p- on 


Cvl 


MJ 


•»■ 


X 




> 


»- at 


o 


>»• 


Cl 


Cl ^ > 


f^ in 


o 


r- 


** 


CM O 


MT 


•4- 


cr 


u 


>■ 


— CJ 


u 


t— t 


• 


* 


• 


# • 


• • 


• 


• 


t 


• 1 


• 


• 


• 


«» 


^ 


i- z 


< 




t-> 


ao 


ao 


oo r- 


m <• 


<M 


UJ 


m 


m in 


mt 


<r\ 


•-• 


UJ 


— 


< < 






w-> 








wt — ■ 


— 1 
















o 


-1 






























u. 


o 


UJ to 






























o 


_) 


CC KTi 






rj 


if 


O <M O 


r- ^h 


in 


m 


in 


oo m 


CM 


m 


—• 




UJ 


< 






<e 


<r 


ifior- 


o o 


<\j 


•-j 


o 


r- er 


•-I 


■c m 


>■ 


> 


x X 




o 


o 


w-l 


p4 


f* v\ 


* * 


o 


Cr 


o 


CM m)- 


cr 


O 


o 


r- 




3 


o 


< 


Cl 


o- 


<* 


-■ o> 


r» ci 


Cl 


co 


•c 


<M M3 


i-i 


r- 


CO 


*-» 


o 


X 


z a 


ITI f^ 


t^ Cl 4- 


ao in r- 


CM 


m 


ci o ci 


o 


«M 


U 


z 


*-i 




o 


• 


• 


• 


• • 


• # 


• 


• 


• 


• • 


• 


• 


• 


a 


3 


X 






■H 


OD 


00 


ao r^ 


■c in 


(M 


cr 


m 


MS M3 


m 


«*• CM 


—i 


o 


< 






t-« 








—4 •— 1 


l-H 














UJ 


or 


X 






























«• 


o 



to • 

IO O 



• UJ 

o o 
uj z 
oc < 
u. or 



^ cm Ci MT m 



rtNW>fin 



•-• cm ci o- m 


UJ 


UJ 




to 


to 




< 


< 




o 


l_> 



125 





+J 




C 




<1J 




c 




o 




Q. 




E 




O 




c_> 




tn 




1 




•>lo 




o o 




«5d" • 




0>» 




i— II 




•> CO 




CL> CO. 




._*: 




ro 




3 • 




cr c 




-C o 


LO 


+j •■- 


C\J 


S- 4-> 


• 


ro =j 


ro 


UJ i — 




o 


<u 


o oo 


r— 


S- 


-O 


4-> C 


PO 


c o 


1— 


a) •■- 




O -l-> 




(O 




i— s- 




UJ Oi 




<L) 




O +-> 




+-> c 




t-H 




s: 




r^ +-> 




o 




E <U 




QJ S- 




+J •!- 




CO Q 




>> 




c/> 




4- 




O 




ai 




to 




c 




o 




a. 




«/> 




a> 




a: 







CJ 






<NJ 


O (Ci o 


o- 


•* 


•* f- rsi r- 


po 


pa 


o ro 


<o a 










•— 








p- m .* 


a 


o> 


o> 


o 


o m 


•— 


ro 


in 


ro 


<\j 


pa 










— 1 


o 




UJ 


m pa or 


O l»- 


p- 


ro 


p«j 


«— t 


H 


pri 


O O o O 










D 


pa 




1/) 


ITNH 


M 


o 


o o o o o 


o o o o o 










< 


P- 




< 


o o o o o 


o o o o o 


o o o o o 










g 

> 
I 


<r 




U 


• • • 


• 


t 


t 


• 


• 


• 


• 


• 


# 


• 


t 


• 










cc 






o o o o 


o 


o 


o o 


o o 


o o 


o o o 










O 










































z 




































co 




a 


•— 




pa 


m —> a 


-H 


*J 


r- 


<* 


jj 


Jri] 


CD 


ro 


cc 


^ 


o 


go 






LU 




< 


0- 






p- en * r- 


w 


-O r~ 


>« 


a 


ro 


m c> 


<c 


m m 






—~ 




UJ 


X 




UJ 


P0 U1 CI 


(M 


•-I 


a 


rn 


Cv. 


M4 


t-» 


MOO 


o o 






(- 




Z 


< 




co 


-*• o o o 


o 


o 


O 


o 


o o 


o o o o o 






BE 




M 


D 




< 


o o o 


O 


o 


o o o o o 


o o o o o 






UJ 




_ 1 






o 


• t • 


• 


• 


t 


t 


• 


• 


• 


• 


• 


t 


• 


• 






a 












o o o o 


o 


o o 


o 


o 


o 


o o 


o 


o o 






D 










































cc 










































Q- 


















































• 


-* 


PO po CP PO 


in 


in 


•o 


o 


^- r\j 


•i 


cr 


0D 


•C P- 






-1 








O O0 


<\] •-< gf 


>!• 


O 


o 


•-■ 


•* 


•o o 


in 


p» 


■£> 


<» 


pg 






< 








UJ 


a 


in •-< «o 


cc 


p> 


r- 


o- 


*— 1 


*-) 


ro 


r-t 


-J- 


<} 


p- 


ro 






C 








a. 


i_> 


mffci 


r- 


<* 


«»■ 


m 


r- 


in 


<r. 


o 


CD 


o 


o ro 






c 








LL 


*- 


o o p* 


^H 


C<J 


CM 


~o 


o- 


(V 


p- 


m 


00 


a 


<o 


in 






X 












• • t 


• 


• 


• 


• 


t 


# 


• 


• 


• 


• 


• 


• 


UJ 
















o o o o 


o 


o o 


o 


.— • 


H 


•■•4 


<*■ 


in 


p- 


o 


o 








































—• 


a. 

o 

u. 












UJ 


• 








































Q 


o 




























O 












a 


z 


•— PO PO, 


^ 


m 


»M 


rj 


ro 


<f 


in 


(H 


O' 


ro 


s» 


in 


< 












X 


o 

<3 




























OC 

o 

LU 

I 
p- 












««. 


CC 


r- ro r- 


LT\ 


cc 


p- 


r- 


r- 


-t 


m 


•o 


•* 


ro 


o 


ro 














Pg Q 


gj- p- gj 


r- 


•* 


ro 


~o 


r» • 


ro 


O 


IT. 


in 


in 


>0 


r- 


LU 
















Co CP co 


o- 


o 


(SJ 


M« 


O 


cr 


-D 


in 


m 


m 


IT 


m 


og 












LL. 


_i 


m o O 1 


t> 


o 


<M 


(SJ 


<M 


pa 


o 


o 


O 


o 


C 


r-4 


ph 












LO 


< 


O s s 


cr 


o 


O 


C 


O 


O 


o 


o 


c 


o 


o 


o 


a. 












< 


rs 


• • • 


• 


• 


• 


t 


• 


• 


• 


• 


• 


• 


• 


• 


< 












o 


p- 
o 


O O O 


o 




■H 




•-• 






■-H 






w~* 




LU 

Z 

-1 




u. 










o 




























a 




D 








^ 


< 


ro r- O 


m 


m 


^ 


-4- 


00 


O 


•o 


•t 


r\i 


-J- 


•* 


>» 


t- 






00 






p-< 


IX 


r- a- o» 


0- 


o 


O 


^ 


<\l 


<f 


CD 


PJ 


rvj 


r%- 


ro 


m 






Z 


z 








O 


eo a a- 


a 


o 


m 


-f 


ro 


rvi 


PJ 


pa 


^j 


#— i 


p4 


p- 


o 




o o 






LU 




o o- o> 


a 


o 


9~* 


m- 


>-< 


*-* 


o 


o o 


O 


o o 


LU 




CO 


_ 






CO 


-J 


o a o> 


o 


o 


o 


O 


O 


o 


o 


o 


O 


o 


o o 


LO 




pa 


t- 






< 


<X 


• #t 


• 


• 


• 


• 


• 


« 


t 


• 


• 


« 


• 


• 


ro 




a 


3 






o 


3 


— o o o 


r-l 


*•< 


—J 


H 


^H 


mH 


*-* 


~h 


*-l 


w—t 


•-i 






< 


_J 








»- 




























LO 




Q. 


O 








U 




























P- 




X 


co 








< 
































o 






































Pa 




u 








N, 






























X 












19 




o •* ~ 


o 


o 


w-t 


fC, 


in 


o 


m 


cr 


•-. 


•c 


•3 


gj 


LU 












< 


o 


CO O O 


o 


^-4 


m 


ro. 


^-t 


00 


<o 


an 


a 


CO 


cr 


C 


_1 












a 


4 


r- o- o 


o 


o 


<0 


r- 


o 


o 


o- 


CO 


a- 


CO 


cr 


v0 


cc 


UJ 










Q 


OC 


•o o> o 


o 


o 


«t 


■* 


LO 


IT 


P- 


CD 


CO 


CO 


CO 


p- 


O 


i_) 












o 


a- o> o 


o 


o 


a 


a 


f 


a 


<?> 


o- 


co 


cr- 


cr 


C0 


OC 


OC 










-J 




• • • 


• 


• 


• 


• 


• 


• 


• 


• 


t 


• 


• 


• 


o. 


o 










< O 


o o -• 


r-4 


r-4 


o o 


o 


o 


o 


o 


o 


o 


O 


o 




LL 










=> 


z 




























o 












P- 






























< 


O 










UJ 






























cc 


«J 










< 






























a 

_J 

< 


CC 

o 

UJ 














o r- m 


o 


CO 


in 


>o 


^H 


«t 


>* 


t-t 


* 


in 


~D 


p- 


r5 


X 












PO 


0* CD s 


•D 


(M 


m 


o 


CT- 


ar 


p- 


cc 


^c 


ro 


LH 


PJ 


»- 


p- 


z 












in co 4> 


O 


<N 


p>j 


wri 


O 


0J 


(M 


in 


CO 


*-* 


P4 


gj- 


o 




UJ 










UJ 


<0 in «*• 


o- 


o 


•»• 


a 


ro 


h 


in 


o 


ro 


cr 


o in 


<I 


LU 


UJ 








L5 


1/) 


m cv rg 


•— < 


PO 


<o 


p- 


cc 


CO 


•o 


in 


-r 


CO 


pj 


rvj 




pg 


» 








< 


< 


i • t 


t 


• 


• 


• 


i 


• 


t 


• 


• 


• 


• 


• 


z 


M 


t- 








at 


<_> 


CD CO CO 


CC 


r- 


m 


(M 


o 


p» 


<!■ 


ro 


ro 


rsi 


OJ 


pa 


Pa 


a 


Ul 








a 










|M| 


w4 


r-* 


















< 


CD 


_ 






IX 






























o 

LU 


LU 

z 


P- VI 






< 




ff<rwp- 


r\j 


a> 


OJ 


OD 


CL 


m 


in 


p» 


CO 


if- 


•C 


H 


pa 


Z UJ 






UJ 


pa 


4JD9EI 


o 


o 


in 


in 


sO 


a 


^ 


ro 


CO 


in 


rvj 


pa 


3 


-J 


UJ 


X 






z 




r\j o cc 


(M 


o> 


•4 


o 


ro, 


X 


co 


O 


ro 


cc 


(\j 


g)- 


a. 




X 


U 






pa 


u_ 


co <o 4 


o- 


a> 


>» 


o 


■C 


LO 


ro 


cc 


OJ 


P- 





•J 


X 


C 


ai z 






-J 


l/> 


a> (m (\i 


•-* 


rvj 


m 


p« 


r- 


CC 


•C 


in 


-)■ 


LO 


*-* 


pg 


o 


►- 


u 


*— 








4 


• • t 


« 


• 


• 


# 


• 


• 


• 


• 


• 


• 


• 


• 


o 




«* 


MP 








O 


CD CO CO 


OD 


r- 


(O 


CO O 


p» 


<f 


ro 


pi 


rvj 


0M 


w* 


aa 


CJ 


-1 


















f-^ 


w~t 


i~* 


















UJ 


a. 


o 




































CO 


o 


CO Z 




































to 


_> 


•— 


3 










r>- r- •* 


m 


f- 


O 


ro 


OJ 


•— < 


•^ 


t— 4 


CO 


cc 


r~* 


m 


< 




o 


u 






-1 




«JO« 


O r~ 


o> 


P» 


>c 


p- 


a 


0* 


o 


an 


ro 


CO 


X 


CO 




a. 






«t 


19 


<■ ^ tr 


«M 


(JU 


f\ 


LT 


(Nl 


(M 


* 


m 


V 


>i 


CO 


•» 




pa 


UJ 


o 






=> 


<l 


o -o >»• 


CP 


a> 


< 


pH 


(NJ 


«g 


PJ. 


p- 


(-4 


P- 


CO 


ro 


X 




> 








t- 


OH 


a- rvi rg 


■— * 


PvJ 


m 


IT 


>c 


r- 


-o 


m 


•*■ 


co 


PH 


rg 


l_> 


>■ 


pa 


u 






u 


LJ 


• tt 


1 


t 


• 


• 


• 


• 


• 


• 


• 


• 


• 


t 


•a 


P- 


p- 


z 






4 




CO CO CO 


CO 


r- 


e\ 


(M 


o 


r- 


<■ 


ro 


ro 


PJ 


rg 


ph 


UJ 


pa 


< 


< 
















wi 


•-H 


•— 


















o 


_l 






































U. 


o 


LU 


LO 




































o 


_l 


a 


CO 










0» r- i*> m 


r-- 


•r 


o 


>!■ 


*-* 


ro 


(M 


-o 


<0 


ro 




Ul 




< 










in m m 


O O 


0" 


CD 


o 


<* 


o 


.*■ m o m 


•— t 


> 


> 


X 


X 








o 


o •-• o> 


fVJ 


co 


o 


m © 


* 


■-( 


pj 


-* 


in 


— I uo 


>- 




=5 








o < 


o**» 


e> 


o 


•-« 


co 


■0 


pg 


p4 


IT 


O 


PM 


g3 


pa 


o 


X 








z a 


<\l fVJ f\J 


*-< 


rv 


t-H 


OJ 


--< 


■H 


p- 


<o 


>»■ 


ONN 


u 


z 


pa 










o 


t • ■ 


t 


• 


• 


• 


• 


• 


• 


• 


* 


• 


• 


• 


o 


3 


X 












0* CO CO 


co r>- 


4 


in 


#— 1 


CO 


•* 


ro 


ro 


ro 


Pu p- 


-J 


o 


< 


















■-I 


mH 


^* 
















UJ 


cc 


X 








co 
co 


• 

o 




























> 
1 


• 
pg 










< 


z 


HN((\ 


^ 


m 


pH 


(Ni 


00 


«»■ 


in 


p-< 


rg n 


g/ in 


UJ 


UJ 










X 






























CO 

< 
U 


co 

< 



oo 



CC <J 
U. CC 



126 



cu 





o 




Q. 




E 




O 




o 




en 

■ 




1 

2: 




r> (^— 




O 




<* • 




en 




1— M 




« co 




(!) CO. 




._*£ 




CO 




Z3 • 




CX £Z 




-E O 


vo 


+J •!- 


C\J 


S- +-> 


• 


A3 3 


CO 


UJ 1 — 




O 


<u 


co 


r— 


s- 


ja 


-4-> E 


ro 


C O 


h- 


CU 1- 




O +-> 




ro 




r— S_ 




lu ai 




cu 




O -M 




+-> E 




1— 1 




nz 




r-» +-> 









E <U 




<u s- 




4-> -I- 




CO Q 




>> 




CO 



CU 
CO 

c 
o 

Q. 
CO 
CU 

cc 














IM 


ya pn a co 


OD 


+ + n « 


tart 


.-rt 


4) PJ 


r» 










•— 








•# ro cr 00 


CO 


tart 





*-t 


pj 


-0 O 


JO 


in 


m 










— 1 


O 




UJ 


tart rO CO 


tart 


ID 


ID 


■c 


•t ro PJ 


PJ 


ta- 1 


OOO 










Z> 






to 


H^IMNH 


tartl 


0000 


O O 
















< 


t- 




< 


•X O O O O 


OOOOO 


OOOOO 










IX 


«I 




u 


• • • 


• 


• 


• 


• 


• 


• 


# 


• 


• 


• 


• 


• 










C 

V 

I 


a 






00000 


OOOOO 


OOOOO 










O 










































z 




































IS) 




a 


1— i 




•-H 


<C J/CD 


^-1 


O 


O "O P- PM PvJ 


ta-l 


ao 


JO PJ 






UJ 




< 


a 






<r r>- f\ m r- 


o> 


4- m fPi 


»~4 


P- CP 


cr 


in 


tart 






tart 




UJ 


X 




UJ 


PJ PJ 00 


•0 


•»• 


^4 


CD 


m 


J* 


fP 


p- PJ 


ta". 


•-i 


tart 






p- 




Z 


< 




10 


IKHO 





f\J 


O 


O 


O 


OOOOO 






or 




tart 







< 


00000 





O 


O 


O O 








O 






UJ 




-1 






<_) 


• • • 


• 


• 


• 


• 


• 


■ 


• 


t 


• 


f 


• 


• 






a 












0000 





O 


O 


O 





O 

















































a 










































a. 


















































• 


taw 


MHO 1 


«Ni 


in 


(Ti 


^ 


a 


>» 


PJ 


J- CP 


ao jo 






_j 








O 00 


rvj — < jj- 


^J- O 





»-rt 


-t 


JO 


O 


m 


p- 


JO 


■* 


PJ 






< 








UJ 


O. 


m .h 00 


00 r- 


1- 


a 


r~t 


ta- 


fP, 


taH 


~f 


>* 


P- 


fO 






Q 








a. 


t_> 


PP. CP CO 


r- 


•* 


>!■ 


re 


t~ 


in 


m 


c 


ao 





»*> 






O 








u. 


w 


tart 


•-» 


Pvl 


P«l 


<0 


a> pj 


p- 


m 


an 


a 


JO 


m 






r 












• • • 


• 


t 


• 


• 


• 


• 


» 


• 


« 


« 


• 


• 


UJ 
















0000 


O O 


^rt 


tart 


tart 


re. 


ir 


p> 





CO 








































tart 


or 



li- 












UJ 


• 








































c 




























CO 















z 


.- 1 pj pe 


•-f 


IT 


^ 


f\J 


ro 


-t 


m 


tart 


rv 


ro 


-t 


in 


< 












X 




< 




























a. 
O 

UJ 

I 
i- 












«v 


or 


P-IMH 


<M 


PsJ 


O 





tv 


tart 


cr 


p- 


p- 


JO 


■£> 


p- 














l\J O 


f-* tart 


•-J 


•O 


ONW 


o- 


p- 


PJ 


a 


JO 


m 


«t 


UJ 
















«0 O 1 (J 1 


0- 


O 


f-- 


* 


a 


a 


pj 


PJ 


0- 


^rt 


JO 


m 


PJ 












UJ 


-j 


P~ CP CP 


a 


O 


IT) 


in 


>!■ 


>* 


.— 


PJ 


^-* 


O 


O 





tart 












00 


<r 


00 G* s 


CT- 


O 


O 


O 


O 








PJ 


r\i 


PJ 


pj 


pj 


or 












< 


3 


• t • 


• 


t 


• 


t 


• 


t 


• 


• 


• 


• 


• 


• 


< 












O K 


OOO 


O 


«M 


ppi 


tart 


■H 


.-rt 


^-1 


•-> 


^rt 


*~* 


^rt 


•_! 


111 














O 




























z 














< 




























-j 




U- 










O 










































>» 


< 


po pn 1-1 


O 


—i 


K 


00 


<o 


ro 





cr 


ao 


co 


m 


r- 






00 






#— 1 


(X 


pn P- P- 


r- 


O 


00 


m 


PJ o- 


m 


p- 


^H 


ao 


O 


a 






Z Z 








O 


pj cr cr 


0- 


O 


o> 


f^ 


J) 


<t 


O 


p- 


in 


pj 





cr 







O 









UJ 




»- cr <r 


a 


O 


PJ 


Psl 


rvj 


PJ 





tart 


.-rt 


O 


pj 


tart 


LU 




1/1 


ta- 






00 


_i 


cr cr 


a 


O 








O 











O 


O 


O 


O 


00 




« 


p- 






< 


< 


• • • 


• 


• 


• 


• 


• 


t 


• 


• 


• 


• 


• 


• 


3 




(X 


3 









D 


tart O O 





ta-« 


•--( 


—I 


tart 


.-rt 


r^ 


prt 


i-4 


•"- 


.-t 


tart 






<I 


-J 








►- 




























00 




0. 


O 








U 




























tart 




X 


00 








< 
































O 






































— » 




<_> 








"V 






























X 

















r- r- 





<o 


f-H 


r~* 


ao 


*-t 


»-l 


ao 


CM 


JO 


»— » 


PJ 


UJ 












< 


CO sO CP 


<3~ 





a 


r- « 


s» 


* 


CO 


■* 


JO 


6» 


rj 


PJ 


-J 












a 


< 


JO CD pe 


a 





»-H 


in 


m 


m 


in 


P- 


00 


cc 


m 


JO 


CO 


UJ 










a 


or 


pj <j> m 


a 





ao 


CO 


cr 


CT- 


in 


(Tl 


p~l 


-* 


in 


m 


















O 


cr a cr 


0- 





ao 


a. 


<r 


oc 


cr 


P- 


P" 


P- 


p- 


p- 


or 


or 










_i 




# • • 


t 


t 


• 


• 


• 


• 


« 


• 


• 


• 


• 


• 


0. 


O 










< 


O 


OOO 





frt 


O 


O 











O 





O 





O 




u. 










3 


z 









































t- 






























<t 













O 






























or 


< 










< 






























O 

_J 
•I 


or 



Ul 














pj .-1 p- 


t>- 


PJ 


ir\ 


in 


_j 





a 


O 


JD 


rr 


a 


r- 


Z> 


I 












PJ 


<r m jo 


ro 


OC 


<0 


in 


00 


PJ 


>» 


ro 





.-< 


re 


«* 


t- 


K 


z 












jo po p-> 


cr 





CP 


** 


O 


m 


o> 


or 


in 


r- 


cr 


m 


O 




UJ 










UJ 


JO pp re 








p« 


a 


-*■ 


^-i 


p- 


CP 


JO 


00 


cr 


p- 


<» 


UJ 


UJ 








O 


CO 


r<i ffl fo 


f. 


in 


p- 


-* 


cr 


P- 


m 


Jj 


-t 


P- 


sO 







PJ 


•x 








< 


< 


• • t 


• 


• 


• 


* 


1 


• 


• 


• 


• 


1 


• 


• 


z 


tart 


t- 








ax 


U 


0* 00 OD 


ao 


r» 


in 


>r 


»-* 


00 


m 


in 


in 


JJ- 


re 


pj 


tart 


or 


UJ 








O 










f-rt 


t-rt 


•-H 


















< 


CD 


^ 






at 
































UJ 


UJ 

z 


t- 00 






1 




P-l »-> O 


>D 


r- 


CO 


in 


00 


ao 


pj 


m 


.-* 


^-i 


tart 


Jl- 


p- 


ta-t 


z 


UJ 






UJ 


1— 1 


a- «n r- 


OJ. 


Pvl 


CO 


m 





a. 


pj 


-* 


p- 


ro 


JO 


cr 


3 


-J 


UJ Z 






z 




rte* 


>1- 


<o 


m 


OD 


in. 


in 


•* 


m 


p- 


m p- 


CO 


a. 




x 









tart 


UJ 


«\i (»> »n 


^rt 


o> 


fNJ 


PO 


m 


O 


tart 


JT 


•* 


cr 


PJ 


in 


X 





UJ 


z 






_J 


10 


00 m 


m 


«» 


fP| 


r- 1 


J3 


in 


m 


p- 


in 


cr 


tart 


p- 





p- 


O 


■— < 








< 


• • • 


» 


• 


• 


• 


• 


• 


t 


• 


• 


• 


• 


t 


CO 




«r 


w 











O 00 OD 


00 


p- 


in 


•t 


^rt 


OD 


in 


«»■ 


«* 


rn 


pe 


tart 


w 





-j 












IH 






tart 


tart 


f-rt 


















UJ 


0. 







































OO 


00 


I/) z 




































10 


3 


tart 


-0 










-< ^ a> «nj 


tart 


rr\ 


O 


p- 


ao 


p- 





P- 


pj 


in 


P» 


< 




a 






-1 




— -0 O r- eg 


m 


re 


m 


a- 


m 


cr 


JO 


CO 





in 


X 


00 




or 






< 





MOV 


« <o 


tart 


0- 


cr 


CO 


tart 


PJ 


cr 


P-I JO 


^■ 




tart 


UJ 






3 < 


o» ^ ro 


w-t 


W 


CO 


* 


f- 


cr 


rrt 


JJ 


p- 


ao 


JO 


pj 


X 




> 








H- 


or 


jcim 


m 


* 


ao 


p- 


p-, 


pj 


fO 


JO ■>»■ 


cr 





p- 





>- 


— 


u 






CJ 


OJ 


• • • 


1 


t 


t 


• 


• 


• 


• 


t 


• 


t 


• 


• 


«* 


ta~ 


p- 


z 






<l 




O 00 CO 


00 


P- 


«r 


m 


•-I 


ao 


u^ 


•» 


JT fO 


m 


tart 


UJ 


tart 


< 


< 










tart 






tart 


ta-i 


r-« 


















(_> 


-1 






































u. 


O 


LU 


on 







































_l 


a 00 










PJ lf\ 


eg 


<o 


P- 


•-I 


in 


in 


in 


CO 


m 


pj 


m 


tart 




UJ 




< 










<« c iri r- 


O O 


pj 


tart 


O 


p- 


cr 


tart 


JO 


m 


> 


> 


z z 











-0 —1 —• 


p- 


«r\ 


* 


J- 


J3 0> 


O 


PJ ^ 


cr 


u 





p- 




D 











< 


fo «r •* 


fi 


o- 


K 





ft 


00 


gj 


PJ 


JO 


^-* 


f>- 


CD 


tart 


O 


X 








Z 


or 


it* ►- r- ft •*• 


CO 


in 


P- 


PJ 


in 


f\ 


p-> 


PJ 





z 


— 










a 


• • • 


• 


• 


• 


• 


• 


f 


• 


• 


• 


» 


• 


• 





3 


X 












tart 00 at 


00 


p- 


<o 


in 


(M 


cr 


m 


JO 


jo m >r 


pj 


-J 


O 


< 












tart 






•-rt 


^-1 


<~l 
















UJ 


or 


X 








to 


t 




























> 
1 

tart 


O 
1 

pj 










00 O 








































< Z 


ta-i <\i m 


«»■ 


Ift 


tart 


po «n 


in 


^■1 


PJ ft 


LU 


111 










X 






























< 



< 




• UJ 

22 

OC « 

u. or 



127 



<u 

c 
o 

Q- 
E 
O 

oo 



CVJ 



<u 



-Q 
re 



•< 


LO 


o 


o 


*d- 


• 


01 




1 — 


ii 


„ 


to 


O) 


QQ. 


j*i 




fO 




3 


• 


CT 


C 


.c 


o 


4-> 


•p— 


S- 


+-> 


ro" 


3 


LU 


p— 




O 


O 


co 


S- 




+J 


sz 


c 


o 


(U 


•p— 


o 


-M 




fO 


p— 


s_ 


LU 


O) 




O) 


o 


4-> 


■!-> 


c 




1— 1 


IE 




r>. 


+J 




o 


E 


CD 


OJ 


J- 


+-> 


■T" 


to 


o 


>> 




c/j- 




4- 




O 




o> 




to 




c 




o 




Q. 




CO 




<u 




q: 









o 






CM 


O'Omf 


00 


00 St 


•4" 


rn 


■c 


*-4 w\ 


«Np 










•- 








■«• O co cr 


<D 


00 — 


o 


•-• 


CM 


•o o 


■o in co 










-J o 




ID 


t-i co v r-* 


tn 


iri -o <r 


pn 


CM 


CM i-i 


o o o 










13 


•— i 




oo 


•* •* CM CM 


•-» 


-> o 


o o 


o 


o o 


o o o 










« 


p- 




< 


-< o o o o 


o o 


o 


O 


o 


o o o o o 










a 


< 




u 


• • • • 


• 


• • 


• 


• 


• 


• • 


• • • 










> 
I 


CC 






o o o o 


o 


o o o o o 


o o o o o 










O 
































z 


























oo 




at 


►— 




f-4 


CO «D O O 


IT 


a — 


CD 


m 


CM 


00 CM 


P- OD f~i 






LU 




< 


a 






co ~* r» cm 


K 


ro »- 


-C 


o 


<£ 


tr tr 


cm cr p- 






N4 




i_j 


X 




UJ 


■oooifi 


fO 


co p. 


<f CO 


CM 


*r — 


*■* o o 






p- 




Z 


< 




to 


IMHOOO 


— o 


o 


c 


O 


o o o o o 






OC 




i^ 


o 




< 


o o o o 


o 


o o o o o 


o o o o o 






UJ 




— I 






u 


• • • • 


• 


• • 


• 


* 


• 


• • 


• t • 






Q. 

O 
a 












o o o o 


o 


o o o o 


o 


o o 


o o o 












• 


,-, 


CM »-l 0> CM 


IT 


WO •£ 


cr 


*t 


CM 


«<• cr 


ac -C r>- 






-1 








O 00 


CM t-t •* -4 


o 


o — 


~t 


o 


o 


tr. p- 


.O ■*■ CM 






< 








UJ 


a. 


IT H tD OD 


r- 


p- tr 


*-< 


r~i 


en 


-H .* 


•4 P- CO 






a 








at u 


co cr en p» 


«»• 


•<t m 


p- 


in 


en 


O 00 


O O ci 






a 








li. 


•^ 


O O —■ < ^-t 


CM 


«M o 


<y 


CM 


P- 


in ao 


cr <c it 






X 












• • • t 


t 


9 • 


• 


• 


• 


• • 


• t • 


UJ 
















o o o o 


o 


o o o 


•-* 


.— < 


—i CO 


m p- o 


u 






























** 


at 
O 
U. 












UJ 


• 






























Q 


o 


















o 












O 


z 


i-i pj m ■* 


IT 


rH (M 


CO 


-* 


m 


-< CM 


ro »»■ in 


< 












X 


o 

< 


















Of 

Q 

UJ 

X 












«». 


a 


HOO* 


fO 


a o> 


p- 


O m 


00 CO 


cr ^ m 














CM O 


(ofi4 4 


a> 


f\J P- 


co 


00 


CM 


tr tr 


00 i-l CO 


111 
















ro ^ ff s 


o 


-* o> 


>c 


<0 


tr 


O O O t-i o 


KJ 












UJ 


-J 


irff a» 


o 


-« p- 


pn 


co o 


•-* pH 


^-< i-l CO 


t— i 












01 «« 


tT 0» O- o> 


o 


o o o 


o o 


o o 


o o o 


at 












< 


3 


• • • • 


• 


• • 


• 


A 


• 


• • 


• • • 


< 












o 


O 

4 


o o o o 




f-> ^ 


^-* 




•-• 


wt —• 


— 1 ■-* I-I 


UJ 

Z 
-I 




u. 










C 


















o 




o 








^ 


< 


O r- s0 p- 


<0 


•O H 


a 


r~ 


* 


•c — 


CM CM CM 


o- 






00 






1— 1 


0£ 


^ 00 CD CD 


o 


in pg 


p- 


-O 


p- 


o -c 


o cr .* 






z 


Z 








o 


«4 o> » cr 


o 


O 0> 


<a 


>o 


«t> 


CM CM CM CM «*> 


Q 




o o 






UJ 




_* 0^ c> c 


o 


CO CM 


CM CM C 


O O O O -4 


UJ 




to 


— 






oo 


_j 


o o ct 1 f> 


o 


o o 


O 


o 


o 


O O 


o o o 


OO 




I— ■ 


(- 






4 


< 


• • • • 


t 


• • 


• 


• 


• 


• • 


• • • 


3 




ct 


3 






O 3 


^ o o o 


f-* 


*-* •— ' 


.-t 


*-4 


*M 


—» r* 


w* i-i «-4 






< 


— i 








i- 


















oo 




a. 


a 








<_> 


















•^ 




X 


n 








< 






















o 




























— • 




(-> 








v. 




















X 












IS 




o <© r^ o 


tr- 


•t sO 


cr 


oc 


CI 


oo cn 


>» -> <f 


UJ 












< 


IS 


r- tr a> o 


«-4 


O O CM 


o 


<0 


o *-> 


cm -< cr 


—i 












a. 


< 


^ o- o o 


O 


cr — 


>o 


•C CM 


o o 


o o en 


cc 


UJ 










o 


(X 


<J» o> o> o 


o 


a> o 


o 


o 


■c 


ao ao 


oo OD tr 


o 


l_) 












a 


f> c> tr o 


o 


oo o< 


a 


cr 


tr 


cr cr 


cr cr cr 


a 


or 










_i 




• • • t 


t 


• • 


• 


t 


• 


• # 


• • • 


a 


O 










< c 


O O O r-« 


t-4 


o o 


o o 


O O 


o o o 




u. 










r> z 


















c 












►- 




















< 


O 










o 




















ac 


•< 










< 




















Q 

—J 
< 


OC 

Q 

UJ 














Hlfl J/N 


tn 


w-t «-4 


— « 


* 


<* 


•* O 


>4 •* O 


3 


X 












eg 


«.Hf04 


rvi 


oc ,-< 


o- 


CO 


<c 


m cr 


p- >© in 


r- 


p- 


z 












a> <o ■* oo 


•o 


O CM 


IT 


cr 


•c 


cr cm 


p- i-i eo 


(J 




LU 










tu 


tf» uo ^f on 


o 


O on 


O 


-o 


ao 


r- cm 


p- cr -t 


«J 


UJ 


UJ 








o 


O0 


IMNNh 


m 


CM O 


U~ 


-0 


in 


tn 4- 


cr »-< cm 




KJ 


:* 








< 


< 


• • • • 


t 


• • 


t 


• 


• 


• • 


• • • 


z 


1— . 


h- 








a 


U 


CO 00 00 00 


r» 


CO CM O 


p- 


■# 


CO CO CM CM -4 


•1 


oc 


IU 








Q 








t-l rA 


rA 












<I 


CD 


as 






a. 




















o 

UJ 


UJ 

z 


1- 


CO 






< 




fO -O oo ro 


00 


tn P- 


o 


CM 


in 


p- tr, 


O cr p- 


r- 


fr* 


Z 


UJ 






UJ 


w4 


oo *h -< in 


CO 


P- O 00 


cr 


^* 


00 p- 


n4 OO CM 


O 


_J 


UJ z 






z 




JjOtOH 


o> 


4 o 


CO 


.* 


•o 


tr >» 


eo co >4 


a 




x 


(_) 






M 


UJ 


oo >c ■*■ (j> 


a- 


•o m 


o 


cr 


o 


4 tr 


m p- cm 


z 


o 


uj Z 






-J 


to 


MVlMrt 


ex 


O CM 


>r 


in 


m 


m co 


cr •-« cm 


o 


p- 


u 


PM 








< 


• t • • 


• 


• • 


• 


• 


• 


t • 


• i • 


u 




< 


w 








u 


OD 00 40 00 


r- 


CO CM O 


p- 


•«• 


en CO 


CM CM -t 


*w 


c 


-1 
















•-) <-H 


•— i 












UJ 


a. 


u 


























to 


to 


00 Z 


























to 


3 


— 


3 










<c «r o m m 


•O CO 


p- 


Ci 


o 


•O CO 


CO ^ o 


< 




O (_J 






-1 




rtr^m* 


* 


CO CM 


c- 


■G 


<o 


■4- ao 


so m co 


X 


OO 




a 






< 


o 


* »- 0> «M 


tr 


r- co 


CM 


r~ 


>♦ 


o m 


inpo 




M 


UJ 


o 






3 < 


■£) <0 *t O 


tr 


p- o 


Ci 


cr 


«t 


sr aj 


4<oo 


z 




> 








p- 


at 


>ONNH 


M 


<c tr 


pM • 


CO 


m 


m co 


cr —> cm 


<_) 


>- 


N* 


u 






<_» 


<_> 


• f t t 


• 


• • 


t 


• 


t 


• • 


t • • 


<l 


p- 


►- z 






« 




oo ao ao oo 


p- 


CM •-• 


o 


r- 


<r 


CO CO 


CM CM i-l 


tu 


1— 


< « 














*-l t-< 


-* 












o 


-1 




























u> 


O 


UJ 


uo 


























o 


_j 


or 


00 










O h- fO ir> 


•o 


P- <♦ 


o 


<» 


— i 


CO CM 


s0 sO CO 




LU 




< 










u> ir ir 4) 


o 


O oc 


o 


<f 


o 


-4 m o in .-< 


>- 


> 


X 


X 








o 


O •-* cr cm 


ao 


© m 


o 


>t 


— i 


CM 4 


m •-• m 


i- 




3 








O 


< 


O o * c 


O- 


O ^* 


CO 


o 


CM 


~4 in 


o -- >o 


~* 


a 


X 








z 


at 


(MNN^ 


<M 


«-• CM 


w~t 


*-> 


P- 


^ sT O CM CM 


o 


z 


•-• 










a 


• • • • 


• 


• t 


• 


9 


• 


t • 


• • • 


o 


3 


X 












0^ 0D CO OO 


P- 


<»■ CO 


— - 


00 


•t 


CO CO CO CM •-• 


_J 


o 


< 
















»■< ~* 


f-l 










UJ 


ac 


JL 








oo 

00 


• 
o 


















> 
1 

-4 


o 
1 

CM 










< 


z 


-« r\i m «» 


in 


rl CM 


m 


«» 


m 


.* CM 


ro sr m 


Mi 


UJ 










X 




















oo 

< 

U 


to 

< 



• UJ 

o o 



ac < 

\L. at 



128 





C i— 




<u o 




c • 




o 




CL II 




E 




O oo 




O CQ 




CO 




z: co 




c 




« o 




O -r- 




^J- +-> 




CTi 3 




i— r~ 




o 




« to 




OJ 




J* c 




fO o 




3 •!- 




CT-M 




-E (O 


00 


■»-> S- 


CM 


s_ cr> 




fO CD 


fO 


LlJ +-> 




c 


Ol 


O •— i 


r— 


s- 


.a 


4-> -M 


(0 


c a 


1— 


<D <u 




c_> s- 




•r™ 




i— Q 




LU 




-o 




o sz 




+-> fO 



<— o 



<u •■- 



+J 


co 


CO 


o 


>> CL 


co 


s- 




O) 


4- 


Q. 


o 


3 




CO 


a> 




CO 


r— 


C 


fO 


o -a 


a. 


o 


oo s: 


a) 




cm 













CP 


O. 


M 


o 


vC 


rg 


>» 


l»- 


o 


>t 


>t 


or 


r- 


UN ^-4 










O 


>» 


P- 


IT 


OJ 


C 


(NJ 


0L 


>c 


<C 


f > 


or 


c 


^ ~> 








00 


-C *D 


r_l 


O 


v_l 


o> 


•£> 


r> 


^ 


4 


•»l 


cc 


c 


■J r»i 




2. 




1/5 


<0 


OJ 


O 


a 


UN 


oo 


t- 


r- 


OC 


*-i 


f. 


m 


LP 


00 — ' 




O 




a 


r- o 


CT- 


>c 


on 


Ol 


w-t 


-t 


OC 


<e 


r* 


r-l 


rr\ 


a- >o 




*- 




to 


• 


t 


• 


• 


• 


t 


* 


• 


• 


» 


• 


• 


t 


• • 




\- 


c 




p-4 


a 


or 


vt 


* 


•£ 


■s 


vt 


(VJ 


o: 


^-* 


.-. 


- 


o o 




W-* 


< 




1-H 




























z 


LO 


a 
































LU 


a o 
































UJ 


a 


































3 


a 


U- 
































r- 


LU 


<I 
































LU M 


a 


IU 
































03 OO 


^> 


z 
































LU 


CO 


•— « 




ir 


c 


CO 


p- 


Ol 


O' 


s 


a 


rr- 


r- 


st 


o 


(NJ 


o a 


Z X 




_J 




pn 


p- 


00 


lO 


OJ 


N 


to 


vl 


«-■ 


o 


a 


9 


*— * 


r- <r 


o «_> 


_J 




CO 


>C 


m 


p- 


•C 


r-4 


•t 


O^ 


o 


m 


m 


o 


00 


ro 


OJ «« 


•- z 


«J 




as 


h- 


4 


«* 


OC 


OJ 


■> i 


r* 


r-. 


f\' 


o 


O 


(Nl 


O' 


tr. h- 


1- ~ 


Q 




< 


IT. 


IT 


>o 


>T 


ro 


«t 


>c 


O 


rr 


vt 


OJ 


m 


IT 


^ o- 


QC — 


C 






t 


• 


• 


• 


• 


t 


• 


• 


• 


• 


• 


• 


• 


t • 


o 


5 






O CO 


CO 


CT 


O' 


»•' 


r- 


eri 


IT 


lO 


OJ 


>^i 


— < 


-■■ o 


k- or 








OJ 


i-l 


*-> 




r-* 


•-^ 


















00 UJ 




































i-i WO 




































Q 00 




































<3 




































C 5 




































Z 


z 


































«- i- 


c 


































cr Z 


»-# 


































a u 


»- 


IS 
































CO o 


< 


< 




r- 


UN 


.— 


-c 


r-> 


Of 


U^ 


><.' 


>* 


OJ 


a- 


>c 


o 


O 4 


< 


a 


a 




00 


O 


LO 


IT' 


o 


r- 


fM 


J 


r. 


or 


•* 


a 


t— 


(NJ UN 


x -^ 


o o 




UN 


CO 


o 


«J 


«e 


en 


rvl 


„( 


o 


rr 


ac 


<o 


(T 


r-> re-. 


3 a 


LU 






>* 


c- 


r < 


00 


re 


>» 


O 


ir. 


or 


vC 


<7< 


o 


4 


\r r- 


r * 


»— 


ct 




en 


p-> 


a 


O r- 


(»i 


#-< 


IT 


00 


•o 


on 


^-1 


rr\ 


O ^ 


*— 


Z «r 




• 


• 


• 


• 


• 


• 


• 


t 


# 


• 


• 


• 


• 


• • 


X 

< 


•— < 


LU 

z 




pj 

•-4 


C 


•— i 


p> 


<o 


r^ 


U^ 


IT 


|»i 


1*1 


-' 


r-l 


-' 


^H C 


i 


K 

LU 
IX 


•— 

-J 





































v» 




z 


oo 


z 


c 


or 


LU 


toil 


00 


UJ 


*- 




X 


M 


O 


h- 


Irt < 


LU 


o 


a 


CO 


a o 


*-* 


a. 




►- oo 


a> 


ee 


Z LU 


a 


< 


LU X 


3 


LU 


X u 


i/i 


z 


UJ z 




— 


O '-' 


_J 


-) oo 


< — 


< 


00 


_J 


a 


< 


a a 


o 




00 z 


X 




— 3 






a u 






a 






LU O 






> 






~ a 






»- z 


z 




*i «. 


u 




-j 


►* 




LU </) 


K 




a oo 


< o 


< 


oe 


< 


X X 


o 


a 


3 


LU Q 


X 


»- 




*- 


z 


or 


X 


ten 


< 


< 




UJ 


X 


H Z 




u 


►-< 




UJ _l 




a 






r— 






o 


oo • 

oo o 
< Z 

X 

• LU 

o o 

uj Z 
OC < 

cl a 



oo o- cu\« 

OJ CC CO T-* OJ 

or fo o- © —< 

«^> o •-* » < u^ 

<y> ro r» fO C' 

• • • • • 

O •-* P» s «o 



•* 


•C 


>t 


OJ Nt 


CC 


O 


o 


c 


»-• 


a 


o 


(M 


X -ij 


m 


(NJ 


o 


CC 


r-< 


■* 


rr 


(T 


— <t 


o 


•_ 


o 


«0 


rr> 


rr\ 


If 


vC 


°? -< 


tr) 


<e 


* 


cr 


^< 


<T 


f 


U" 


r-> <£ 


r- 


o 


o> 


IT 


vO 


• 


• 


• 


• • 


• 


• 


t 


• 


• 


re 


O 


r~ 


UN OJ 


in 


>* 


(NJ 


P»J 


o 


—t 


^^ 

















r* pi oj O oj 

^ ro o. o oj 

>>■ 0D r- (NJ —i 

00 UN ON (NJ Ol 

O ^J" O- U\ rr> 

• • • • • 

UN O f" r- oj 

** oj «-• — t w\ 



*-* 


OC 


CJ 


a- 


f- 


•— < 


C 


0> 


if' 


•o 


UN 


CO 


r- 


a- 


PI 


ON 


(NJ 


^ 


mO 


o 


O 


o 


r- 


-t 


^ 


t 


• 


t 


• 


• 


*c 


UN 


o 


CT 


IT 


^^ 


.-« 


—> 







ir . O O or. ►• 
oo o o o o 

l-><0 ^IC <0 
•* OJ ON fO ro 

on oi on oo h- 
• t • • • 

oo o oo a- •£> 



s UN PN ^- OJ 

— OJ * n* 00 

00 9 r- O on 

O INJ O Ol «o 

4 H (0 h <C 

• • • • • 

«* O O- «0 ON 



-4 O; ON >* UN 



i-Mm^ir 



OJ 



O* ON Oj >C 0* 

0- 0C vO ON CT> 

O OC ON o- rr\ 

■4- >o r~ o p» 

C CO OJ C7> P- 

• • • • • 

liN ^ C> rt CJ 



OJ ^ f-i OJ <* 

<c n ^ or if 

r-< C 00 •-* Pi 

on <r »f , oj p- 

0- O O P- <i 
t • I t » 

UN tf f»> v O 



—> OJ P", »t UN 



PN 



UJ 

o 

CC 

o 



< 

Q. 

a 

LU 

X 



CL 

<r 

LU 

z 



LU 
00 

3 



> 

r- 
*—> 

o 
o 

-J 

UJ 

> 

o 

z 

3 
CJ 

ac 

o 



129 





e ir> 




oj o 




e • 




o 




Q. II 




E 




o to 




O CQ 




00 




z: to 




e 




•> o 




O -r- 




^ -M 




cr> 3 




r - ^~ 




o 




•» 00 




<L> 




-^ E 




rC O 




3 T- 




cr+-> 




-C 03 


<T> 


+-> i. 


CVJ 


S- CD 


• 


ro <u 


CO 


LU +J 




E 


CD 


O M 


r— 


s- 


jd 


4-> +J 


CO 


E O 


1— 


O) CD 




O i- 




•r— 




r— Q 




LlI 




-o 




O E 




+J rd 




_l E 




r- O 




•P - 




E +■> 




<U •■- 




+J to 




to O 




>> Q- 




oo s- 




<1) 




tfr- Q_ 




O 3 




OO 




01 




to i — 




E ro 




o -a 




Q. O 




to s: 




01 




cc 











»-" 


»-< 


ir 


rr 


r-< 


O 


— < 


in 


fr. h- 










00 


00 


c 


If 


c 


*• 


>0 


00 


»-< 00 








to 


a 


vC 


r> 


QC 


00 


<£> 


cr 


a 


>C r^ 




Z 




to 


ir 


>c 


00 c 


r-" 


m 


•4 


>*■ r- r\i 




o 




a 


10 


.-* 


c> 


O 


»-t 


a 


r~t 


>*• 


ret O 




•— < 




LO 


• 


• 


• 


• 


• 


■ 


• 


• 


• • 




fr- 


(J 




ct 


r» 


v0 


J- 


If 


>* 


CO 


ro 


fM —J 




•—1 


<r 






















z 


uo 


a 






















LU 


c 


O 






















LU 


a 
























3 


a 


a. 






















fr- 


u 


<T 






















ill — . 


a 


u 






















ec oo 


33 


z 






















LU 


oo 


•— 




CM 


00 


cvj o 


r- 


a 


a 


r> 


C' vf 


2 X 




_J 




if r~ r- o c^ 


r- 


r- 


r- 


r- o 


o o 


_J 




to 


if' 


to 


o 


ro 


r- 


•& 


O 


ir, 


o o 


•— z 


< 




CP 


on 


o 


LC 


ct 


tr. 


v0 


u\ 


4 


^ <T 


fr- .-. 


O 




< 


<*• 


CT 


c 


ro 


ro 


t- 


N 


o 


»^ CT" 


CL — 


o 






• 


• 


• 


• 


• 


• 


• 


• 


• • 


O 


X 






r~ 


CM 


ro 


CD 


o 


or 


Lf \ 


vD 


>J CO 


fr- 10 








w-l 


*•< 


.-1 




•— ( 










OO LU 


























*- 00 


























o oo 


























< 


























c z 


























z 


z 
























i- fr- 


o 
























ee z 


•— 
























a. u 


fr- o 






















to o 


< 


< 




oo 


CM 


ct 


r~ 


oc 


00 


r 


O 


o> u. 


<. 


Of 


or 




r- 


ct 


rvj 


rvi 


r*i 


r- 


J 


O 


o »0 


z -> 


o c 




ct 


ct 


ac 


oo 


r- 


r- 


o 


<i 


»-• 00 


D O 


LU 






_i 


<t 


o 


o 


ro 


cm 


r- 


c 


rr, C 


z < 


fr- 


CC 




f-i 


«4" 


or 


a 


ro 


■£> 


f- 


o 


o o 


»— ■ 


z < 




• 


• 


• 


• 


t 


• 


• 


• 


• • 


X 


M 


LU 




ec 


r- 


r» 


if. 


«£ 


If 


m 


«* 


r«"i <\i 


«r 




z 






















z 


fr- 
o 

U.I 

CL 


»— 1 

-J 























4 4 4 H P 

if . h- r- ^ a 

* ff * Cl M 

C -J >C * Ui 

O «C h- U"\ co 

• • • • • 

.-■ c c o o 



if O fo t-i <0 

if if m if if 

— • if rvj rr if 

ir. c o oc ^ > 

rr> t- <r >e •» 

• • • • • 

-H c a c o 



ro •-• s C* ro 

-4- «£ C» »- »-• 

>0 0> ro oo ^ 

rr CT- ^ >i> <o 

^-4 >C h- if ro 

• • • • • 

** o o o o 











00 


*-* 


vf 


vf 


•-i 


ro 


*p4 


Cs.' 


rr 


r- 


—) 


r-l 


o 


<C 


r-i 












r\j 


T- 


rr 


rsj 


o 


(\) 


>C 


o 


v0 


oc. 


c 


LO 


CM 


<t 


CT 


LU 








00 


•C 


<s 


>o 


r- 


00 


fi 


^5 


r- 


O 


rrt 


>C 


CT 


r- 


if 


CM 


O 




z 




oo 


r-t 


ro 


o 


O 


f-4 


if 


>» 


ro 


r* 


rg 


If 


O 


r- 


— i 


If. 


CC 


z 


a 




oc 


r~ 


a. 


<>■ 


-J- 


t-l 


^-4 


CC 


ir\ 


O 


0- 


ro 


ro 


nO 


CT 


ro 


a 


LU 


•— < 




O0 


• 


• 


t 


t 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


LU 


LU 


fr- 






o 


r> 


r- 


r- 


tr 


CM 


or. 


•c 


<t 


W-* 


m 


OJ 


»-4 


O 


O 




3 


M 


o 




w—t 










»-< 




















o 


fr- 


CO 


<r 


































< 


LU 


O 


a 


































oc 


CC 


a 


c 


































a 


*» 


oc 






































fr- to 


LU 


or 


































LU 


Z LU 


a 


<r 


































X 


LU X 


=3 


uu 


































»- 


a. o 


to z 




03 


>r 


•— " 


lf 


r- 


00 


>» 


o 


>J 


o 


m~\ 


If 


CT 


fv. 


•V 




LU Z 




^- 




o r\' 


oc 


rc 


m 


r\i 


in 


■— 1 


00 


a 


O 


1/' 


C 


r- 


If 


LK 


l~> *- 


-J 


_j 


oo 


ir\ 


■— i 


o 


rvj 


r- 


o 


ro 


ro 


r- 


o 


<o 


O 


ro 


n0 


If 


M 


< w 


< 




CO 


if 


oo 


>*■ 


ao 


if 


•4 


r- 


<3 


J" 


o 


—< 


•4" OJ 


«!■ 


r- 


•— , 


_l 


o 




< 


ro 


ao 


o 


r> 


rr, 


r^ 


^H 


o 


CM 


o 


«» 


Lf 


CT 


*-* 


* 


OC 


a. o 


o 






• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


# 


< 


u) Z 


z 






«T 


r- 


rr, 


>j 


O 


ro 


CM 


o 


r- 


ro 


m 


CM 


•— i 


r-\ 


c 


LU 


— 13 








■H 


—< 


*~i 


t-> 


h 


— i 


r-l 


















z 


O □ 






































^-t 


a. 






































-1 


lu e> 








































> 






































o 


— o 






































fr- 


fr- z 


z 






































■d «. 


u 




































<_) 


-J 


•— ■ 




































LU 


LLI tO 


fr- 




































00 


oc to 


< o 




•o 


if 


ro 


>c 


00 


sD 


<0 r» 


lt> 


If 


r<- 


CT 


<t 


If 


ro 


15 


< 


oc 


< 




«vj O 


ou 


rv 


r<> 


C 


r- 


r> 


>c 


-0 


■-I 


ro 


CT 


— 1 


— i 




z z 


O 0C 




If 


o 


cr 


r- 


r» 


r- 


if, 


o> 


00 


ao 


r- 


>!- 


O 


rvj 


* 


00 


3 


LU 


o 




t»- 


ro 


>-> 


a 


^ 


o 


rsi rvj oo 


Cr 


oo 


O 


«* 


ro 


<o 


*— 


Z 


fr- 






rvj 


C 


rvj 


ao 


ro 


r» 


** 


v<J 


C\J 


d 


ro 


«M 


<o 


rj 


fO 




tea 


z oc 




• 


t 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


> 


X 


•— > 


< 




00 


00 


OD 


r- 


>o 


<VJ 


00 


If 


>»• 


CM 


ro 


CVJ 


r-< 


o 


o 


fr- 


< 




LU 














-J 




















— - 


z 


fr- z 


































o 




u 


>— ■ 


































O 




LU 


-J 


































-I 




oc 




































LU 




— « 




































> 




a 


00 


• 

o 
































Q 

Z 






< 


Z 


•—I 


rv 


ro 


<t 


»f 


•— ' 


<M 


ro 


<f 


If 


t-t 


<M 


rr, 


^ 


If 


C 






Z 


































CC 






• 


LU 






































O O 






































LU Z 


r-t 










fM 










ro 
















OC 


«X 






































LL 


QC 



































130 



Z 

LU 
UJ 

3 
»- 

ff 

z 
c 



OO 

z oo 
c a 

>~ oo 

t- c 

•— < 

oo a 

Ci C 
a 

a. a 

a <r 

a \, 

rs z 



r\j cm r- .-* cr 

•-i a oc co «c 

u- co <y -4 ■>€ 

m cr cm co >4 

>* CM <0 CM «C 

• t t • • 

—i .4 in f- mj 



<* r- 


If 


cm 


»-< 


O 


< 


•+ -4 


00 


OD CM 


f 


r-< 


cr 


a 


o 


eo m 


>c 


CO ^ 


rr 


00 


r- 


^ 


m 


-* -o 


CM 


-C m 


r- 


cr 


<4 


•* 


r- 


CM CM 


<C 


<C co 


cr 


p- 


IT 


•-j 


a 


(T CO 


4 



in co rr ^ <f 



+-> 




c 


^— 


CD O 


c 


• 


o 




a. 


II 


E 




O 


to 


o 


oa 



OO 





« O 




o •■- 




"3- +-> 




CH =3 




r™ r— 




o 




* oo 




CD 




-* C 




ro O 




13 -r- 




cr+J 




-C (T3 


o 


+•> &_ 


co 


S- CT> 


• 


CO CD 


co 


UJ 4-> 




c 


at 


O •— i 


r— 


S- 


JD 


4-i +J 


CO 


c: o 


h- 


CD CD 




<_> s_ 




•I— 




r— Q 




UJ 




-o 




O C 




4-> ra 




s: c 




«5f O 




•i— 




E -M 




QJ -r- 




+-> O0 




O0 O 




>, a. 




00 s- 




a; 




m- a. 




O ZJ 




oo 




a 




in i — 




E (O 




o -a 




a. o 




oo s: 




a> 




a; 



CC *- 

a 

»- 00 

00 tu 

•— oo 

O ui 

< 

Z 

•— K 

OC Z 

oo <_> 
< 

o a 

z: < 

< 



< 
o 
o 



oo 

cc 



co> .-> «-i ^ c 

-O CM •£> «-i O 

00 MT. O >} 

cm r- CT or »t 

oo* c vf)o» 

• • • • • 

CT f» <-< CM •— 



-c cr ^ o vO 

O in r- cv .£> 

0P CM CV C\J -4> 

0> co cm or if 

<0 in cm ** oc 

• • * • • 

C m r- oc r- 



z 
□ 

h- e 

< < 

ct & 

O Q 
UJ 

I- OC 

Z «r 



o 

UJ 

o 



Ci IT «* U^ «» 

ro O <C ^-« O 

o <i ir o in 

• • • • • 

CM C". >f< «C ^ 



t-i IT. f ■ CM OP 

00 t^ «o O |fi 

Hfl0Ol^>J 

~< ^ CM >J- N 

v0 •-« 00 —t CO 

• • • • • 

r- C) <j m in 



»-* O r-< r-l »-« 



ff O « >t IT' 

t- f» o o r- 

oo so »f cm r- 

nj >t cr f>- «o 

oo cm >C '-' on 

• • • • • 

,J H H W H 



ITi Cf fl 4 CM 

IT fj> 4 O f\J 

cm h- o> o- in 

cr —» >t in ro 

ph c m cc in 











CM 


in 


a 


\t 


cr 


CO 


00 


nO 


r-H 


n 


in 


t 


CM 


CO 


CO 












CM 


<J- 


r-j 


o 


-c 


r- 


r- 





CC! 


cr 


a 


u\ 


a 


o 


>0 


UJ 








00 


>* 


rvj 


•* 


o 


<c 


t-H 


rr 


ro 


f 


r~ 


co 


CM 


o 


o 


CM 


u 




z 




oo 


O 


<T 


« 


r- 


>* 


m 


ro 


o 


r- 


st 


CO 


C 


ir. 


-c 


>c> 


oc 


z 


o 




cc 


© 


t-« 


CT 


cr 


<. 


r- 


if 


f, 


ir 


in 


in 


vf 


ifi 


r-i 


vT 


o 


UJ 


^-4 




oo 


• 


• 


• 


• 


• 












• 


• 


• 


• 


• 


u. 


UJ 


»- 






m 


^-j 


cr 


r- 


•>c 


>C 


rri 


r-< 


oc 


Nt 


o 


m 


>r 


ro 


f-< 




2 


H4 


e 




•— i 


^-i 








~i 


•-* 


f— 1 
















o 


»- 


oo 


«3 


































•a 


UJ 


c 


a 


































a 


cc 


a. 


Q 


































o 


— . 


cc 






































1- 00 


UJ 


cr 


































UJ 


Z LL, 


o. 


< 


































X 


uj X 


Zi UJ 


































»- 


s: o 


oo Z 




cr 


00 


ri 


m 


o 


oo 


o 


>J- 


Hi 


o 


ao 


.-i 


CM 


CM 


U 




uj Z 




•— i 




m 


CM 


fO 


t~* 


o 


r-i 


cr 


rr 


r<> 


•0 


r- 


r- 


vf 


cr 


r- 


UJ 


o •- 


-1 


_J 


00 


a- 


m 


»-i 


*o 


* 


ft 


r-( 


00 


in 


•* 


■4 


>o 


■4 


o 


r- 


ki 


< w 


4 




CO 


«t f» 


o 


<T 


«* 


oc 


ro 


r- 


O 


m 


O 


cr 


r- 


m 


vC 


»— ■ 


— 1 


a 




< 


tn 


sO 


r-t 


in 


cr 


00 


O 


rr> 


nj 


cc 


CM 


r- 


00 


«ti 


co 


a 


Q. O 


o 






• 


• 


t 


t 


t 


• 


• 


• 


t 


• 


• 


• 


■ 


• 


• 


•a: 


00 Z 


z 






m 


r- 


>0 


m 


i— i 


CM 


<c 


•4 


CM 


r- 


r^ 


in 


4 


rn 


^-* 


UJ 


— 3 








CM 


•— * 


^-< 


— < 


»~i 


CM 


—) 


•-I 


—< 














z 


Q U 






































►-* 


a 






































-J 


UJ o 








































> 






































o 


«- Q 






































K 


»- Z 


z 






































^ «l 


u 




































u 


-J 


t-l 




































UJ 


UJ oo 


K 




































oo 


OC oo 


< o 




O IT 


-J- 


o 


>* 


r-t 


00 


m, 


vt 


00 


o 


cr 


r- 


CM 


CM 


Z) 


< 


CC 


< 




<-i 


i-j 


m 


ao 


>t 


<*> 


fM 


>* 


ro 


CO 


ro 


CM 


ro 


ro 


CM 




I X 


o CC 




tH 


ro 


in 


in 


o 


CM 


m 


in 


m 


* 


O 


CM 


in 


CM 


in 


00 


3 


UJ o 




•H 


in 


v0 


vO 


m 


cn 


CO 


>c 


wi 


r* 


m 


in 


CM 


ro 


CO 


•M 


*■ 


►- 






o 


CM 


CM 


ro 


•-< 


o 


o 


O 


o 


co 


m 


*t 


in 


CO 


in 




M 


Z Of 




• 


• 


• 


• 


• 


• 


t 


• 


• 


• 


• 


• 


• 


• 


• 


>■ 


X 


*— t 


< 




CM 


•— i 


cr 


oo r- 


<o 


in 


CM 


oc 


in 


sD 


ir> 


>r 


CO 


•— 


r- 


< 




UJ 




fH 


^-1 








t-l 


■-4 


<~l 
















•— ■ 


X 


u 

UJ 

cc 
o 


z 
— 1 

oo 
oo 


• 

c 
































O 

o 

-J 

UJ 

> 

Q 

Z 

r> 






<x 


z 


•-1 


CM 


c- 


st 


»n 


^-> 


CM 


CO ^ 


m 


K-l 


CM 


ro 


Nf 


in 


c 






z: 


































cc 
a 






t 


UJ 






































o o 






































u- 


z 


»-l 










CM 










CO 
















(X 


< 






































u. 


cc 



































131 



CO 
CO 

JQ 
rO 



+J 

C IT) 
CU O 
C • 
O 

Q. II 
E 
o to 

O QQ. 

to 

z: to 

c 
•> o 

O i- 

^t- +-> 

CT> 3 

O 
"CO 

CU 

-* c 
rC o 

3 T- 

o-+-> 

-c re 

+-> 5- 
i- CD 
fO CU 

LU 4-> 

c 

O HH 

s_ 

+-> +-> 

c u 

O) cu 

o s- 

•I— 
r— Q 
LjJ 

-o 
o c 

+-> rO 

S c 

«* o 

E -£ 
CU t- 
4-> tO 
to O 
>> Q- 
l/O S- 

QJ 
M- CL 
O 3 

CO 
CU 

oo 1 — 
C rC 
O "O 
Q. O 

oo s: 

CU 



Z 
Uj 
UJ 



u — . 
CC to 

u 

Z I 

o u 



CC —■ 

o 

t- to 
oo uj 

•x OO 

O on 

< 

s: 



Z 00 

o a 
•-> oo 

t- O 

•- < 

to Ct 

c a 
a 

a. a 

uj < 

a. uj 

3 Z 

oo — 



<M IT vO •♦ mD 

>fr 0C P\j c- O 

"O c< IT «\l 

MOOMT < 

• • t • • 

o> f. «t it. m 



n a ci >o «o 

^- «\j re <f * 

IT •» * r- to 

r- m .£> <\; *0 

oo in cm c-< it. 

• • • • • 

p-, <\j pn s» c- 



o 
o 

5. 



o* 

co 



vO ec it —» r- 

CD 1^ ffi C^ ff 

h- <t 4 b a 

U> IT «~m P- *£> 

(M IT PO «* CM 

• • • • • 

o o o ■ o o 



f- -4 If ■ nO in 



z 

0. 
oo 

a: 

x 

CM 

X 

< 
i 



< < 
or of 

c o 

U.I 
c- CC 

z < 

z 

t- CM 

tj _i 

UJ 

a 

CM 

a 



o 


cr 


>c 


O 


H 


00 


o 


m 


a 


ro 


r\J 


<c 


r\j 


o 


in 


oo 


r-M 


0* 


IT> 


r~ 1 


in 


C* on 


f- 


o 



mC IT P- IT 


ir, 


rr. >© «1 O 


n 


HH OD <0 


CT 


«* O O r- 


Ml 


in cc O •* 


C4 



on eg ri in <£> 



r <v -4 >* m 



«m cm «\i cr ir. 

O «* ni <\i o> 

>» f> o <* r- 

r-< oo r- *o -c 

i»- m r- o on 

• • • • • 

C O O c- o 



«o m 


p- m 


a 


CT> rrt 


r> 


rv 


O 


or o 


on <m 


r- 


cr o- 


-n 


in 


c 


C on 


vl- ~< 


cr 


>C fM 


o- 


<r 


m 


>c o 


in ro 


o 


in a 


r-H 


vC 


ir 


to o 


r^ fv 1 


r- 


CM o 


o 


r\j 


^-J 



erf O w* •"* H 



f*- o 


in o 


4 


a cr 


<£> >t 


t- 


u. on 


o o 


o> 


rvj >J 


in ao 


*~* 


r- «0 


CO o 


<T 



O O O cm o 











.*■ 


o 


•* 


H 


«0 


cr 


fri 


O 


fi 


sO 


r> 


P<J 


r- 


m 


m 












a- 


in 


<c 


r» 


o 


r- 


m 


a 


00 


oc 


r- 


U v 


^ 


oc 


a 


UJ 








oo 


c-l 


>n 


o 


«0 <M 


ir 


o 


r<-> 


o 


in 


PA 


<\J 


-t 


PSJ 


r- 


o 




Z 




00 


on 


c« 


o 


0> 


CM] 


&■ 


90 


rr 


vt 


-o 


CS.I 


o 


in 


H 


vC 


cc 


z 


o 




cc 


cM 


■f) 


r\j 


-M- 


<£) 


r\j 


r-~ 


r- 


(V 


in 


co 


PvJ 


•J3 





oc 


o 


UJ 


CM 




oo 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


t 


• 


• 


• 


• 


u. 


UJ 


1— 






>*• 


o 


cr 


r~ 


in 


* 


H 


a- 


r- 


pr, 


P0 


co 


rv 


CM 


o 




JT 


CM 


c 




—t 


^-j 








c4 


— 1 


















O 


c- 


00 


< 


































< 


UJ 


c 


CL 


































cc 


CO 


a 


a 


































o 


!■» 


cc 






































r- CO 


UJ 


ex- 


































UJ 


Z UJ 


a 


it. 


































X 


UJ X 


z> 


a. 


































r- 


£ U 


oo Z 




f\ 


p* 


<i/ 


r- 


r~ 


H 


F~< 


oo 


<y 


cr 


(f- 


in 


f* 


oc 


o 




uj Z 




— 




O 


in 


o 


H 


CO 


<c 


>o 


4- 


o 


p- 


ao 


r^ 


CX 


m 


o 


UJ 


O CM 


_J 


-J 


oo 


m 


in 


CT\ 


h- 


o- 


r~ 


CT 


o 


~t 


a 


CM 


fM 


f. 


ao 


PO 


ISJ 


< — 


< 




CO 


«-> 


m0 


o 


c4 


<o 


C\J 


in 


>t 


oo 


cr 


>* 


CT 1 


r- 


^i 


in 


CM 


_l 


u 




< 


CM 


00 


>r 


m 


H 


0*1 


r- 


r~ 


sO 


p- 


m 


m 


or, 


nj 


— i 


CC 


a o 


O 






• 


• 


• 


• 


• 


• 


• 


• 


• 


t 


• 


• 


• 


• 


• 


4 


oo z 


z 






m 


in 


«-• 


nj 


o 


CO 


pn 


c-» 


CT 


IT 


sf 


P0 


rj 


C\J 


r-4 


UJ 


— Z) 








f\J c- 


—• 


—i 


CM 


cH 


CM 


f-M 
















z 


CJ o 






































CM 


CC 






































-J 


uj o 








































> 






































o 


cm a 






































r- 


t- z 


Z 






































^ ^ 


M 




































LJ 


-j 


CM 




































UJ 


UJ oo 


h- 




































00 


cc oo 


< o 




m 


>o 


on 


w4 


H 


CO 


r- 


m »0 


in 


fi 


r- 


o 


>» 


si- 


Z3 


< 


CC 


< 




CM 


CM 


re 


oo m 


<M 


o-l 


p- 


O 


rsj 


00 


o> 


r- 


«VI 


p- 




i a- 


O CC 




m r- 


P0 


CO 


l/» 


f" 


PO 


pi", 


in 


o^ 


pn 


a 


-» 


o- 


CT 


oo 


rs 


UJ O 




O ^ CsJ 


>t 


c4 


«M 


>r 


>£> 


oo 


-o 


0> l>- 


>t 


r- 


CM 


CM 


X 


c- 






rr» o>> 


CM 


»M 


<r 


O 


p~ 


CM 


PO 


w-< 


<r 


CM 


o 


00 


o> 




» 


z a 




• 


• 


• 


• 


• 


• 


• 


• 


• 


» 


• 


• 


• 


• 


• 


> 


X 


CM 


< 




C 


00 


CO 


00 


MJ 


««• f\J O O 


m 


PO 


pn 


<M 


CM 


o 


r- 


< 




UJ 














CM 


CM 


d» 
















M 


Z 


UJ 

cc 

CM 

o 


Z 

l-M 
-i 

OO 
O0 


• 

o 
































o 

_J 

UJ 

> 

o 

z 

3 






«s 


z 


H 


f\J f" 1 


«* 


m 


CM 


PVJ 


ro 


>* 


m 


■M 


CM 


rn 


vj- 


m 


CJ 






a: 


































cc 
o 






• 


a- 






































a 


a 






































LU 


z 


d 










OJ 










PO 
















CC 


< 






































u. 


Or 



































132 





+J 




E r— 




cu O 




e • 




o 




Q. II 




E 




O to 




o oa 




oo 




■z. to 




c 




* o 




O •!- 




**■ +■> 




CM Z3 




l™~ l^ - 




O 




« CO 




O) 




-^ E 




ra o 




3 T- 




CT4-> 




-E (O 


CNJ 


+J S- 


00 


t- cn 


• 


fO QJ 


OO 


LU +-> 




e 


<u 


o »-. 


r— 


s- 


jQ 


-(-> +-> 


03 


E O 


h- 


QJ CU 




o s- 




•r— 




r— Q 




LU 




•o 




O E 




+J CO 




IC E 




r-« o 




■r™ 




E -!-> 




(U *- 




+-> to 




CO O 




>> Q. 




CO s- 




(U 




4- Q. 




O 3 




00 




ai 




00 i — 




E ro 




o -a 




Q. O 




to s: 




<u 




cc 











PO 


OD 


O 


co on 










O 


uv 


CO o «j- 








CO 


«0 


IT 


ec 


c ■* 




z 




CO 


CO 


CO 


ro 


CO «-> 




a 




tt 


w* 


«0 


m 


^ tr- 




•— • 




CO 


• 


• 


• 


• • 




K- 


c" 




PO 


vt 


>* 


on »Ti 




»—i 


< 












z 


to or 












LU 


c a 












LL. 


a 














3 


a. 


a. 












»- 


a 


< 












u — 


a 


u 












CD l^ 


2 


Z 












LU 


CO 


—• 




sO 


<r 


,- 


•* o- 


Z T 




_J 




LP 


vt 


•c 


st fp 


O c* 


_) 




CO 


4- 


00 


•£ 


*-• >* 


*-* *- 


<T 




(T 


03 


-c 


•C 


LP -4" 


r- *-> 


c 




< 


r^ 


cr 


s0 


P» -h 


ac <— 


o 






• 


• 


• 


• • 


O 


x 






m 


f- 


>c 


CO c 


r» 0O 














— « 


C« Ut 
















•— to 
















Q to 
















< 
















o x 
















z 


z 














•— i- 


a 














or. Z 


•— ■ 














a u. 


»- o 












to o 


< 


<T 




*■ 


m 


m 


IT PJ 


< 


a: 


Of 




oo 


t-> 


cr 


CC 00 


X -> 


O 


o 




00 


oo 


r-1 


»o o 


3 o 


LU 






vC 


ac 


p- 


«o o 


X <• 


r- 


at 




(V 


>* 


cr 


r- m 


•— < 


z <r 




• 


• 


• 


• • 


X 


i— 


UJ 




f\J 


4 


tM 


•* r- 


«x 




Z 












x 


►- 

LU 

ac 

*-* 
c 


-J 













M 00 M rH i-l 

^ oo i-i r- ^J 

fV r-t 4^ O 00 

<© 4- <\j f\i r» 

O co >t >t <f 

• • t • • 

w-> oo m >t cn 



o O^ (7> cn r- 

ro m o* C —» 

a «C cc o tr\ 

(M 4 ^ tr (<"i 

M * H < O 

• • • • • 

O O *~> #-- «M 



n <t cr h>j 

O o"* •-< O t*- 

>£> «0 <4" •"-! PJ 

r- m p- a m 

ct> cr. c no <?• 

• • t • • 

>-'«*• cn «c p» 



p- C rn PJ •-• 
«C CT> O p- ni 
po C o "" oc 
IT, rn _, (<p ^) 
p-v (T «t 00 ro 
t « • • • 
OOhhn 



vO O «T PJ O 
O* (Vi iC >C <J 
IT* -4 C >* O- 

p- cn «o vO p- 

m ro cn ^. m 

• • • • • 

p»i m p> st cn 



a >o o c p- 

4- on o^ p- 4 

oo p- ^i o cn 

m p- tf\ (?• p- 



o o ^ 



i CO 











or 


4 


v0 


ro 


cn 


r> 


c- 


s* 


<0 


vl 


t— 4 


CO 


c 


in 


h» 












o 


r- 


m 


p- 


4 


p- 


•*; 


ro 


u 


or 


o 


fp 


cr 


rvi 


t-H 


LU 








CO 


•4- 


vT 


p- 


y 


<f 


o 


(T- 


oc 


o 


oc 


o 


«— I 


O 


vt 


ro 


*_' 




z 




to 


PO 


K 


p- 


p- 


ft 


o 


■f 


no 


ec 


p- 


no 


p> 


p- 


s0 


r^. 


a 


Z 


o 




or 


«» 


P0 


m 


rr 


o> 


pi 


IT 


CT 


Cl 


4 


cn 


pp 


p- 


%c 


O 


a 


LU 


M 




to 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


LL 


LU 


1- 






PO 


•-i 


a 


p- 


in 


v*- 


ro 


t— i 


cr 


cn 


cn 


in 


4 


m 


co 




3 


*— 


15 




r-« 


-^ 








•— < 


f-i 


i—i 
















CO 


K 


CO «I 


































< 


LU 


o 


a 


































CC 


CO 


a 


a 


































o 


•~ 


ac 






































t- CO 


LU 


or 


































LU 


Z LU 


a 


<r 


































X 


LU X 


3 


UJ 


































»- 


z. o 


CO 


z 




««- 


O 


a 


cn 


cr 


o 


u^ 


c. 


a 


>» 


cn 


cn 


•4 


p- 


,-1 




LU Z 




»— • 




O 


o 


^^ 


oc 


ro 


p» 


O 


rr> 


o 


p- 


o 


•J 


—4 


cr 


pi 


LU 


O •— 


-J 


_) 


CO 


<o 


4 


•0 


cr 


>r 


CM 


Cvj 


*r 


-o 


CM 


CM 


a 


vO 


r-l 


CO 


PO 


<I w 


< 




CO 


o 


m 


^-i 


CO 


«* 


>r 


p- 


<j 


m 


cn 


in 


cr 


00 


>t 


03 


►— " 


-J 


a 




< 


in 


p> 


>r 


m 


<-4 


o- 


cr 


•— » 


ui 


LP 


o 


<i 


ao 


cr 


ro 


ac 


o. a 


o 






• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


• 


^ 


CO z 


X 






CT 


in 


r\j 


CO 


o 


p* 


in 


m 


p— i 


p- 


*o 


ir. 


4 


m 


CO 


cu 


— 3 








r-t 


—i 


p^ 


r-l 


t-l 


•^ 


»-i 


r- 1 


r ( 














z 


Q U 






































•— ' 


cr 






































■J 


LU O 








































> 






































o 


<— o 






































►- 


1- z 


z 






































^ «l 


u 




































l_) 


_) 


•— 1 




































LU 


LU CO 


»- 




































to 


OC CO 


< o 




P0 


.— i 


P- 


r~ 


CVJ 


cn 


in 


•-I 


o 


c- 


o 


•c 


a 


a 


p- 


13 


< 


oe 


< 




>t 


m 


vC 


m 


cc 


<o 


IT 


on 


CO ^t 


rr. 


o 


•-J 


rp 


st 




X X 


o 


OL 




>o 


m 


•— i 


cr 


o 


t> 


>t 


o 


m 


o- 


a 


cn 


p- 


cr 


IT. 


CO 


z> 


LU O 




4} 


ro 


m 


o 


c 


P0 


0- 


>* 


i-i 


p- 


o> 


03 


00 


cr 


P- 


M 


X 


t- 






ro 


m 


rr 


co 


cn 


p- 


<f 


cr 


p- 


P1 


vC 


<r 


p- 


vC 


o 




KM 


z a 




• 


■ 


• 


• 


• 


# 


• 


t 


• 


• 


• 


• 


• 


• 


• 


> 


X 


•-i 


< 




o< 


co 


oo 


00 


p- 


cn 


>r 


—j 


00 


cn 


cn 


irv 


■♦ 


ro 


CO 


r- 


< 




LU 














w* 


»-< 


r-< 
















■-4 


X 


o 

ID 
CC 

a 


Z 
-J 

CO 


• 
































U 
O 

-I 
LU 

> 

£3 

Z 






to a 
































3 






« 


z 


•-• 


CO 


m 


«4 


cn 


ft 


CO 


ro 


4 


cn 


<— i 


P0 


ro 


-4 


cn 


O 






X 


































ac 

o 






• 


LU 






































a o 






































LU 


z 


r-l 










PO 










ro 
















CC 


< 






































U. 


or. 



































133 



















«* 


l/i 


r\ 


•£/ 


r, 


«M <T. 


<t 


CC 


o 


a 


O 


p- 


-< o 




















co 


cr> 


cc 


r~ 


rg 


C". fO 


r- 


QD 


r-< 


h 


CM 


o- 


o- ir 


















to 


CO 


r-l 


c* 


m 


♦Vi 


a s» 


o 


ir 


—4 


«*• 


fi 


c 


— c 














Z 




oo 


T* 


«t 


0> 


■JO U"v 


-* o 


in 


co 


C»> 


>* 


o 


■•■ 


f-4 V 














a 




at 


CO o» 


(T 


<o 


«* 


CO o 


CO 


r^ 


<c 


pH 


•J- 


r~ 


O CM 














»-* 




00 


• 


• 


• 


t 


• 


• • 


• 


• 


• 


• 


• 


• 


• • 














»- 


O 




•-» 


m 


m 


sf 


in 


O «\j 


cv 


f 


>1 


o 


o 


o 


«-• t-< 














•— 


< 






































z 




O0 O' 






































u> 




O Q 






































UJ 




a 








































3 




(X 


a 






































►- 




UJ 


< 






































UJ 


«■» 


a 


UJ 






































CD 


on 


2 


~z 








































UJ 


to 


•— • 




p- 


CO 


r- 


vfl 


in 


r^ rr> 


in 


c 


a 


© oo 


vt 


o >t 










Z 


X 




_J 




a 


(V 


CO 


ro 


h- 


nj «4 


<\j 


f- 


o 


p~ 


p- 


o- 


.-> en 










o «_> 


—1 




to 


en 


J- 


o 


CM 


4 


C^ in 


rr 


o 


o 


cr 


r- 


cr 


p- o> 










» 


z 


< 




CO 


>t 


a> 


•-• 


^ 


or 


«v in 


«C 


CT 


f- 


^-i 


cc 


nn 


r-' <C 










t- 


•— ' 


a 




< 


CM 


cc 


<NJ 


•c 


^■i 


m in 


f— < 


•• « 


in 


CM 


U\ 


CC 


— «t 






_ 




ac 


*■* 


o 






• 


• 


• 


1 


• 


• • 


• 


• 


• 


• 


• 


• 


• • 






+J 




o 




X 






re 


v0 


</ 


r^ 


o> 


f-i to 


vf 


ir 


-o 


o 


o 


c 


— r-l 






£Z 


in 


K 


0^ 






































0) 


o 


«/> 


UJ 






































c 




■■4 


O0 






































o 




o 


00 






































Q_ 


n 




*z 






































E 




C? I 






































O 


to 


z 




z 




































<_> 


ca 


a 


Z 


er 




































CO 




a 


U' 


r- 


13 




































• 


00 


u> 


< 


< 




T-t 


ro 


*-* 


«H 


in 


ro «m 


CM 


^r 


•* 


p~ 


>o 


in 


CM O 






ZT 


to 




< 


CC 


Or 




■* 


a 


<x> 


f»> 


«M 


fV CC 


O 


*4 


^ 


ro 


<J 


ao 


r_> in 








c 


X 


~» 


o 


O 




m 


^ 


r- 


>!■ 


>o 


ro «o 


c 


in 


«c 


CM 


c 


<f 


in re' 






n 


o 


3 o 


LU 






o> 


00 


r-4 


r\j 


o 


cc a 


r- 


in 


OP 


>© 


>£ 


O 


»c >t 






o 


•r— 


x 


< 


*- 


a 




in 


N 


IT\ 


>*- 


(T, 


0> (^ 


cr- 


r~> 


in 


i— i 


vt 


00 O CM 






•3- 


4-> 


•-* 




z «t 




• 


• 


• 


• 


• 


• t 


• 


• 


• 


• 


• 


• 


• • 






<y\ 


3 


X 




>— 1 


LD 




—t 


pr> 


rv 


d 


r- 


O f\J 


CM 


vt 


>*■ 


o c 


o 


w-4 w-f 






r "~ 


'o 


< 
x 




»- 


z 

>— 1 


































n 


co 






O -J 


































<L) 








UJ 




































J^ 


c 






a 




































co 


o 






•— 




































Z3 


•1— 






c 




































cr+-> 










































-C 


03 








































CO 


4-> 


S- 








































CO 


S- 


C7> 








































• 


03 


O) 








































CO 


UJ 


-l-> 

c 








































<D 


o 


1— 1 












vO 


O 


o O <NJ 


r- «vj 


r~< 


P- 


o- 


<r 


r- 


00 


m o 




^~ 


J- 














<o 


-J 


o» 


cc 


»NJ 


r- o 


•4 


o 


r— 1 


cc 


u~ 


pH 


■~c in 


LU 


-Q 


+-> 


+-> 










OO 


>* 


CO 


IT 


o 


fS» 


>* o 


CM 


<o 


•—I 


>*■ 


in 


>0 


00 o 


<_) 


(T3 


c 


u 






z 




00 


m 


p« 


vO 


o> 


If- 


>r «*> 


-J- 


cr 


cr 


CM 


a 


CM 


.♦ in 


C£ 


1— 


ai 




z 




n 




CC 


a 


rr 


r^ 


vTi 


-* 


f*< CO 


<f 


O 


«0 


«*• 


CM 


o- 


CM CM 


Q 




o 


uu 




~ 




00 


• 


• 


• 


• 


• 


• • 


t 


• 


• 


• 


• 


• 


• • 


li- 






■r™ 

a 


UJ 




K 






p»4 


o 


(T 


r- 


in 


CM .-I 


c 


CO 


>* 


ro 


tn 


CM 


nj »■* 






^~ 


3 




«— ■ 


e 




r J 


— < 








— ' w4 


•— • 














C-S 




LU 




1- 




00 


<i 






























< 






"O 


Ul 




O Of 






























cc 




o 


sz 


CO 




OL 


Q 






























o 




+-> 


03 




a* 


a. 






































o 


>~ 


OO 


UJ 


or 






























UJ 




z 


u. 


a 


< 






























X 




UJ 


Z 


3 UJ 






























H- 




E 

a> 

V) 

>> 
to 


-l-> 


X 


«-> 


00 


z 




CM 


(Nj 


ITN 


(SJ 


in 


O CM 


o 


r~ 





>t 


«— i 


«» 


in sj- 






UJ 


z 




•—i 




lf\ 


m 


O 


J- 


p- 


r~ r- 


CM 


p« 


o 


t-t 


m 


U 


cr- cn 


Uj 




to 
o 

s- 
ai 

Q. 


u 


— 


■J 


— i 


oo 


* 


<\J 


O 


cu 


^ 


>J CO 


•*j 


rvi 


o 


-0 


<o 


-o 


o a 


rsj 




< 


w 


< 




CO 


m 


o 


n0 


a> 


CO 


r- nJ- 


m 


CO 


p- 


m 


.— i 


cr 


fn ^3 


*— 




_J 




CO 




< 


#— i 


a 


p- 


>j- 


r-t 


r* --O 


rri 


r^ 


m 


p» 


in 


cr 


«» ^ 


OC 




a 


o 


o 






• 


• 


• 


# 


* 


• • 


• 


• 


• 


• 


• 


• 


* t 


«t 




00 


z 


i 






CO 


>j 


^H 


^-4 


o> 


m ro 


r-H 


tr 


vO 


rn 


en 


fxj 


CM —> 


UJ 




<+- 


"■* 


=3 








•— " 


w < 


—> 


•-* 




— i ^ 


i-i 














z 




o 


3 


o c 


































"^ 






CO 




Q. 


































—J 




<u 




UJ 


CU 






































to 


,_ 


> 




































a 




c 


03 


•-• 


(J 


































r- 




o 


"O 


h- 


z 


z 




































a. 


O 


4 


4 


u 
































i_i 




</) 


s: 


_J 




tart 
































UJ 




CD 


UJ 


CO 


►- 
































to 




CC 




B 


00 


« O 




1-4 


in 


<t 


t>- 


m 


r-< ^4 


t-l 


^C 


>!■ 


«*■ 


o 


«♦ 


•4 C 


O 










< 


or. 


< 




•O 


r-t 


re 


^ f\J 


CC —. 


a 


or 


sO 


m 


o 


p» 


<o in 










X 


X 


o a 




IT> 


4) 


«T 


CO 


■c 


O CM 


m 


o- 


<o 


o^ 


CM 


r~ 


*•> m 


OO 








=5 




UJ 


c 




ID 


in ><■ 


oc 


o 


O CO 


o 


>o 


CO 


r* 


CnJ 


p- 


a >i 


•— 








X 




K- 






CM 


<VJ 


ro 


f-4 


<*! 


CM (r 


in 


•c 


in 


m 


V*" 


cr 


wm «M 





Z Ot 



UJ _J 
ct 



CO CC CO CO P- 



Hi N O N <J 

<-" pH r-l 



CO PO CM CM t-t 



o 



UJ 

> 



oo • 

oo O 

< z 



• UJ 



oc < 

u. a 



hnci <t ir 



t-t cm m ^ m 



CM 



t-t cm c^ sj m 



m 



3 
O 
cc 
o 



Table 3.34 



134 



Hydrodynamic Parameters for System 4, Mid-Frequency Range, 



El Centro 


Earthquake. 


3 = .02 in 
s 


Each Mode 


Parameter 


Node 


Including 

[c s Kx g } 


Excluding 
CC s ]{x g } 


*l x sLax* 


1 


18.95250 


18.98743 


(inches) 


2 


16.31281 


16.37181 




3 


13.45125 


13.47894 




4 


12.30791 


12.21299 




5 


10.53108 


10.50990 


«|x s l» 


1 


6.28175 


6.26993 


(inches) 


2 


5.21131 


5.20904 




3 


4.48454 


4.48830 




4 


3.75600 


3.75798 




5 


2.81634 


2.81841 


{ l*sU } 


1 


32.53683 


32.50833 


(in. /sec) 


2 


23.84686 


24.27509 




3 


19.37517 


19.68547 




4 


21.22523 


21.28960 




5 


15.38559 


15.47496 


{<|x s |» 


1 


10.26027 


10.26663 


(in. /sec) 


2 


7.95916 


7.94259 




3 


6.83778 


6.82866 




4 


5.61321 


5.60034 




5 


4.52049 


4.51665 



C\J 





CVJ 


4-> 


-M 


4- 


»+- 


J 


CVJ 


U 


O 


o> 


CU 


to 


to 


D_ 


D_ 



— 

•p- 



+-> 

(_> 

CL) 
LO 
I 

Q- 



135 



o 

CU 
CO 

-o 



03 



-o 

03 



CO 



co 

J- 

O) 



o 



CD 

■o 

O 



u 
It) 



oa 



CO 

ai 

4-> 

s- 

a> 

O- 

o 

s- 



03 

s- 

+J 
O 

S- 
4-> 
00 





















, — 


■3- 


CO 


CD 


*r 


o 


, — 


LO 






















CO 


co 


«* 


CO 


r^ 


CVJ 


cn 


r-- 


r^. 


1^ 


lo 


*t 


CO 


CO 


^J- 


O 


CD 


<d- 


CO 


cn 


o 


"3- 


LO 


CO 


CO 


00 




• 


• 


r-~ 


r-s. 


LO 


co 


<3" 


r^ 


«d- 


CNJ 


<n 


*d- 


^f 


CVJ 


CVJ 


r-^ 


r— 


oj lo 


ro 


CM 


O 


LO 


LO 


CO 


CD 


*d- 


r-^ 


O 


«3- 


<tf- 


p— 


CO 


LO 


r— 


T— 


-a co 


CD 


ro 


i — 






r— 


CO 


o 


r— 


















o 


«=d- 






i 




i 




*fr 


CD 


CNI 


o 

00 


o 
1 


cvj 
1 

o 


CVJ 
1 

«3" 


en 

CVJ 

i 

o 


00 

CVJ 


«3" 

CVJ 
CD 


z: 






*i- 


o 


CO 


00 


O 


co 




CD 


o 


CO 


«tf- 


00 


CVJ 




CO 


CO 


CO 


CM 


i^ 


CO 


CO 


o 


cn 


n— 




CO 


o 


m 


CVJ 


CO 


r--» 




CO 




• 


• 


ro 


<3- 


«=f 


CO 


CO 


r^ 




CO 


cr> 


LO 


o 


CO 


CO 




o 


<JJ o 


CD 


r^ 




I — 


r— 


r— 


CO 


CO 




CO 


o 


00 


00 


r— 


<3- 




o 


"O CO 


LO 


^— 










CO 


CO 


















• 


O r— 


CVJ 












i 






o 


o 

CO 


i 

CD 


cvj 
1 

o 


CO 

CNJ 

1 

o 






CVJ 
CO 


z 






«* 


CO 


cn 


r— 


00 






r^- 


r>» 


CO 


r^ 


CO 






CO 


LO 


a-) 


CO 


CD 


1-^ 


to 


i— 


CO 






CO 


r«-. 


*d- 


r— 


o 






o 




• 


• 


^J- 


00 


00 


o 


1^ 






lo 


o 


C\J 


CVJ 


*3- 






LO 


CU LO 


CO 


CO 


n— 


r— 




oo 


o 






t— 


<3- 


CD 


cn 


o 






CD 


"O CD 


r— 


^~ 








CNI 


CO 




















• 


O r— 


CVJ 






1 




1 








o 
o 


CM 

i 

*3- 


CNJ 
1 

00 


CO 

cd 


LO 
CO 






«3- 


2: 






r-^ 


CO 


r^ 


o 








*d- 


*3- 


LO 


CO 








CO 


^d- 


CVJ 


CO 


^~ 


<n 


CNJ 


Lf) 








i — 


CD 


LT) 


CO 








r^ 




• 


• 


>^- 


LO 


CD 


CNJ 








CM 


t— 


00 


r— 








t— 


a; o 


r - 


LO 






"3" 


CO 








I-- 


r^ 


CVJ 


o 








CVJ 


-o CO 


r^ 


r— 






CNI 


LO 








• 


• 


• 


• 








• 


O CNJ 


i™ 




co 


i 

CNJ 


1 

CO 










r— 
1 

CVJ 
«3" 


CO 

1 

«3- 


CO 

1 

00 
CVJ 


LO 
LO 








■3- 

CD 
LO 


CO 


LO 


«5j" 


ro 


CO 


**• 










r^ 


CO 


CO 










LO 


CD LO 


• 


• 


CO 


CO 


<tf- 










CO 


o 


CO 










CVJ 


-a cvj 


CO 


*d" 




CO 


00 










C\J 


CD 


CO 










LO 


O CO 


*d- 


r— 




CNJ 


«d- 










• 


• 


• 










• 


2: 


1 






1 












*3- 


LO 


00 

*3- 










o 

r— 









r^. 


«3- 


r-^. 


CO 


CNI 


fx. 


• 


• 


CO 


LO 





CD 


CD 


•vf 


CO 




1 


«^- 



>) 

00 





















^~ 








CD 




• 


• 


CD 


II 








«=*" 




CO 




CO 


-C 


CO 




r— 


+J 








D_ 








<D 








Q 








S- 


II 


II 


II 


<u 









<TJ 



a) 

2 
o 



n h 



/_■ 






CO 


CVI 


>5 


CVJ 


*d- 


oo 


CO 


CD 




CD 


LO 




CO 


r^ 




CD 


CO 




1 — 


"* 





CVJ 


cvj 


CD 




1 — 


CD O 


r^ 


"O CD 





O CO 



CO 



^3- 

LO 
CVJ 

o 

CO 

CO 
CO 



r^ 


1 — 


CVJ 




LO 


CU LO 


CD 


-0 r-^ 


LO 


rj- 



CVJ 







II 


CD 




> 




O 




-Q 5- 




< O 


T 


O 
E 1— 


3 


O U- 


U 


•r— 




03 03 




> CU 




a> 




<— 



CM 
4-> 



136 



CM 



U 

CD 
CO 

I 
Q. 



CM 



O 
CD 
CO 
I 
Q. 



4- 



Q. 



O 
CD 

I 
Q. 



O 
CD 
CO 

-o 

s- 



CD 

3 



O 
O 



























LO 


LO 


r^. 


O 


CTl 


CM 


*3" 


LO 








^a- 


CTl 


r-~ 


CO 





r^ 


LO 


CM 


^3" 


CM 


r-. 


O 


CM 


O 


CTl 


r-^ 


r— 


CO 


LO 


CO 


r^ 


CO 





LO 


LO 


00 


CM 


LO 





CM 


LO 


CM 


LO 




• 


• 


CM 


r— 




CM 


CM 


CO 


«* 





CO 


*d- 





00 


LO 


CM 


LO 


CD 


CO 


CO 












en 


00 


LO 


r— 


O 


>3- 


"vl- 


CO 


LO 


h- 


-a 1^ 


lo 


«*■ 












^— 


r^~ 


































1 


1 







O 


O 





CO 


r^ 


O 


00 


2: 




















r«- 


r^ 


CM 


1 


1 


CM 

CO 


CO 


CTl 








CO 


1-^ 


i^» 


LO 





CO 




LO 


r^ 


t^v 


LO 


5- 


r— 




00 


LO 


^— 


^3- 


CO 


CO 


CTl 





CM 


LO 




CO 


ro 


CM 


*3" 


O 


r— 




00 




• 


■ 


LO 


1— 


CM 


LO 


CM 


LO 




CO 


LO 


CO 


00 


LO 


LO 




CO 


CD O 





LO 










LO 


•* 




r-» 


CO 


CO 


I — 


CO 


CTl 




00 


-a 


n— 


CO 










1— 


CO 


















• 


O CM 


CTl 












1 








LO 



1 


CD 
1 

CO 


«3- 
1 

LO 


CTl 
CM 


CO 

O 




CM 




2: 

LO 






r— 


00 


CO 


LO 


CO 






CO 


■vj" 


r-~ 


I— 


«3- 











LO 


CO 


LO 





CO 


LO 


«3- 






CO 


CTl 


CO 


CTl 


CTi 






1^. 


CD O 


• 


• 


CO 


r— 


CO 


r— 


^- 






LO 


CM 


CTl 


O 


r-~ 









-0 CO 


00 


O 


t— 






^T 









^" 





"5* 


r^. 


CO 






CM 


O CO 





CO 








1 — 


CO 




















• 


2: 


r^. 








1 


1 








O 


CM 

1 


"3" 
1 

CTl 


CM 
1 


CO 

CO 






CTl 


*3- 






en 


LO 


LO 


CM 








CO 


CO 


r^. 


O 








r^ 




1-^ 


LO 


CM 


00 


LO 


CTl 








r^. 


en 


CM 


00 








LO 


CD O 


• 


• 


00 


r— 


CO 


CTl 








1^ 


LO 


<d" 


CM 








LO 


-a LO 


CM 


CO 




^— 


"3- 


en 











CTl 


co 


LO 








co 


«=i- 


O 


CM 






CM 


CO 








• 


• 


• 


• 








• 


2: 


•=d- 




CO 


1 

CO 


cr> 










CO 

1 

CTl 
LO 


LO 

1 

CTl 
CO 


CO 
CM 

1 

O 

CTl 


O 
1^ 








00 

CM 


CO 


LO 


^- 


co 


CO 


«3- 










CTl 


CO 


r^ 










CM 


CD LO 


• 


• 


CM 


r>» 













«5j" 


*3- 


CO 










LO 


"O CM 


CO 


^- 




CO 


cr> 










co 


CM 


CTl 










CM 


O LO 





r— 




CM 


■3- 










• 


• 


• 










■ 


2T 


CM 






1 












«3- 


CTl 


1^. 

LO 










LO 









r^. 


■=*• 


r^ 


CO 


1^. 


O 


• 


• 


r^ 


LO 


O 


CTl 


LO 


^~ 


CM 




1— 


«* 


CM 




1 





CO 





















LO 


O 





CTl 




• 


• 


CO 


II 


O 





O 




CO 




*3" 


-C 


CO 




r— 


4-> 








Q. 








CD 








O 








i- 


II 


II 


II 


O) 








+J 








3: 


""7 


n 








2: 


^ 


r— 1 


00 


Lx 


u 


1 1 


i. 








CD 









CO 

CO 
CTl 

LO 


LO 
CO 
LO 
O 
CO 


O 

CM 

1 


LO 


CTi 

en 




1 — 




<3- 

CO 





CO 



o 



CO 






CM 


CO 




CM 


CD O 


r^. 


"O CTl 


•=d- 


O LO 



CO 



LO 




^ 


CD LO 


00 


-O (^ 


LO 


O LO 


LO 


2Z 



II 


CD 




> 




O 




JO s- 




<=c 


rj 




C 1 — 


3 


O Ll_ 


*_j 


+-> E 




(O fC 




> CD 




CD O 




1— O 



4- 



o 

to 
I 

Q. 



CM 
-M 



CM 

o 
<u 
to 



ex 



4-> 
4- 






a 

a> 

to 
I 

Q. 



137 



CD 

to 



-a 
as 

s- 



cu 
c 
+-> 

E 

o 
o 



«3- 
a> 
























LO 


, — 


LO 


CTl 


LO 


CO 


•zt 


CTi 








^J- 


LO 


CM 


«=J- 


CO 


LO 


r— 


CM 


CTl 


CTi 


LO 


CTi 


CO 


CO 


O 


r-^ 


CM 


CO 


co 


r— 


CO 


CO 


r-«. 


LO 


LO 


LO 


r— 


LO 


CM 


Kt 


«3- 


CM 


CO 




• 


" 


i — 


^~ 


CO 


CM 


LO 


«d" 


*3" 


r^ 


i — 


LO 


CO 


00 


r-^ 


1^ 


00 


a> o 


«d- 


CM 












LO 


CM 


<3- 


CM 


CO 


r— 


CO 


CO 


CO 


00 


-a o 


^d- 


r-^ 












^— 


LO 


















O i— 


i — 










1 




I 




o 


O 


O 


r— 


CO 


LO 


1 — 


00 


z: 




















CTi 


LO 


LO 


1 
CTi 


1 

LO 


CM 

1 

CTl 


LO 


r— 








r-^ 


*fr 


«* 


*d- 


CO 


CO 




r^ 


I-- 


CTl 


oo 


LO 


CO 




1— 


LO 


^ 


LO 


r-^ 


r— 


co 


r-» 


r^. 


r— 




LO 


LO 


CM 


o 


LO 


o 




LO 




• 


• 


CO 


i — 


i— 


CO 


CM 


"3" 




CM 


O 


CO 


r— 


r-~ 


o 




CO 


a> o 


r^ 


CM 










CO 


CM 




r-. 


O 


«=*- 


00 


i— 


*3- 




*t 


-o r-s. 


cn 


LO 










r— 


CO 


















• 


O CM 


r^ 


















o 

CO 


O 

1 

CM 
CM 


o 
1 

CO 
CO 


CO 

1 

CO 


CO 
CO 

1 

CTi 


co 

CTi 




o 

CO 
LO 


z: 

LO 


r— 


LO 
















r-^ 


CO 


1 — 


LO 


r— • 






r-^ 


a> o 


• 


• 


CO 


o 


CO 


en 


LO 






CO 


CM 


cr> 


LO 


cn 






^— 


-a o 


ID 


o 


r-» 


LO 


cr> 


r— 


LO 






LO 


LO 


^d- 


o 


CI 






>=T 


O -53- 


LO 


LO 


r-^ 


CM 


r— 


i^ 


LO 




















• 


z: 


r-. 








' 


1 


CO 
CM 






o 

CTi 


O 
CTl 


CM 


CM 

CM 

1 


CO 

CO 






CO 
LO 


<3- 






O 


CTi 


<* 


o 








co 


CTi 


O 


i — 








■vf 




LO 


LO 


r— 


LO 


>vf 


cr> 








CTl 


•vi- 


«3" 


n— 








o 


oj lo 


• 


• 


LO 


CO 


LO 


cn 








r— 


CM 


LO 


LO 








o 


T3 CTi 


00 


cn 


c— 




CO 


CO 








-3" 


O 


LO 


CM 








CO 


O LO 


r— 


*3- 






T— 


CM 








• 


• 


• 


• 








• 


z: 


lo 




CM 


1 
CM 


1 

CO 










CM 

1 

LO 
LO 


LO 
1 


CO 

1 

o 

<T> 


LO 








LO 
CO 

1-^ 


CO 


CO 


r— 


CM 


CM 


<3- 










CO 


LO 


«3" 










CTi 


CU LO 


• 


• 


«3" 


r— 


co 










CTi 


00 


<tf- 










o 


-a cm 


cr> 


i-^ 




«d" 


r-^ 










CO 


LO 


i— 










CO 


o r^ 


CO 


CM 




CM 


CO 










• 


• 


• 










• 


z: 


CM 




LO 


1 

CO 




• 

E 








LO 
CO 


CTi 
1 

LO 


CO 
LO 




E 

>> 






LO 

o 

CO 


CM 


LO 


r-~ 


<* 


cr 




CO 








CO 


CO 






CO 






«3- 


CO o 


• 


• 


CO 


«3- 












LO 


^r 












o 


-o cti 


CO 


r— 


LO 


r— 












LO 


CTi 












CTi 


O I--. 


LO 


r— . 


^— 


^> 












• 


• 












• 


z: 


1 




1 














CO 


LO 












CM 





4- 

o 
o 

CO 

II 

4-> 

Q. 
CD 
O 

S- 

a> 



o 






o 

CO 
CO 



■"7 



o 
o 



«* 

LO 
CTi 
CO 






CO 
LO 
CT) 
**■ 

CM 
CO 



CJ 



LO 


i — 


«3" 




r— 


CD LO 


CM 


-a r^ 


«^- 


o co 





ai 


ii 


> 




o 




J0 s- 




<c o 


'~T 


o 

E i — 


3 


O Ll_ 


Z_i 


•r— 
4-> C 




ns to 




> cu 




cu o 




i— o 



CM 



CM 



CM 



o 

o» 
to 


O 
to 


Q. 


Q. 






-M 

\ 
O 
CU 
to 

I 

Q. 



138 



o 

CU 
to 

-v. 
■a 
ro 





















CM 


ro 


CTl 


o 


o 


CM 


LO 


ld 








LO 


r^ 


<o 


r^. 


lo 


LO 


LT) 


LO 


r-. 


1^ 


a> 


en 


CM 


r^ 


ld 


r-. 


CO 


ro 


LO 


LO 


r^ 


LO 


LO 


r^. 


cr> 


CM 


CO 


CM 


en 


o 


LO 


o 


en 






• 


r— 






CM 


ro 


<d- 


LO 


10 


■ — 


O 


^~ 


LO 


o 


t— 


CM 


O) o 


LD 


CO 












CM 


I-*. 


LO 


CM 


i— 


r^. 


ID 


«d- 


ro 


CM 


-o o 


CO 


CO 












r— 


CM 


















O CM 


cn 














I 




o 


o 


o 


o 


un 


o 


CO 


lo 


z 


CM 




























<3- 


r-» 


■ — 









CM 


CO 


CO 


o 


CO 


LO 


r^ 


CO 


ID 


CM 


o 


CO 


cn 


r— 


• 


• 


CO 


r— 


CM 


CO 


CO 


LD 


LD 


en 










r— 


CO 


■3" 


lo 










r— 


CM 


LO 












1 









i — 


r^ 


i — 


CM 


o 


=3" 


CO 


CM 


«3- 


LO 


O 


o 


• 


• 


CO 


CM 


r— 


CM 


CM 


CO 


«vT 








r— 


CM 


cn 


LO 








r— 


CM 


CM 








1 


1 





-o 
CU 

3 
E 



O 

o 



"3- 

r0 







r— 


CM 


CO 


CTi 


Cn 


o 


CO 


^J" 


CO 


CO 


• 


• 


*d- 


00 


ID 


CTl 


CO 


r^. 


n— 




CO 


CO 


in 


•3- 






r— 


CM 


CO 






1 


1 





CO i— 



. 


• 


CM 


CM 


r^ 


CO 


r>. 


r-^ 


1^". 


en 


CO 


CM 


CO 


o 


CM 


CO 






«3- 

CM 

1 


CO 



■ — r-~ 

lo i— 

CM 



cn «3- 

cn id 

i^ CO 

LO •— 

r— «vT 
I 



E 

00 



cn 


CM 


cn 


cn 


o 


cn 


cn 


■=3" 


r— 


CO 


r-* 


CO 


^- 


j— 


cn 


o 


CO 


cn 


ID 


LO 


CO 


CM 


LO 


CM 


CO 


O 


CO 


CM 


r-^ 


o 


o 


O 


o 


«3- 
1 


co 
i 


^- 


CO 


LO 


ID 


ID 


r«-» 




cn 


*3" 


n— 


cn 


ID 




LO 


O 


CO 


LO 


CO 




CO 


■^1- 


1— 


CO 


r^ 




*d- 


O 


ID 


•— 


r-~ 




o 


1 


CO 
1 


CTl 
CM 


Lf) 

cn 




r^» 


r-^ 


CO 


cn 






o 


00 


*d- 


CO 






CM 


lo 


«=1- 


en 






CO 


LO 


<3- 


cn 






LO 


■ — 


«3- 


CO 






• 


• 


* 


• 






CM 


LO 


CM 
CM 


00 







«*■ 


CO 


, — 




o 


ID 


CM 




CO 


O 


<3" 




o 


CD 


LO 




ID 


>* 


i — 




• 


• 


• 




r-^ 


CO 


CM 




i 


CM 
1 


LO 


• 

E 


en 


LD 




>> 


i^. 


ID 




CO 


un 


O 






<tf- 


^— 






ID 


i — 






• 


• 






o 


«3- 






CM 


LO 







LO 


LO 


CO 




CO 


a> o 


en 


-a o 


i — 


o *d- 



cn 



CO 


LD 


CM 




r~- 


CU O 


«* 


-a o 


ID 


O LD 



LD 



o 


^r 


LD 




r-. 


CL) LO 


CO 


-o cn 


<d- 


o r-^ 



CM 


CO 


<=t" 




CO 


CU LD 


LO 


-a cm 


r— 


o en 



CO 



1^ 


CM 


CM 




CM 


CU O 


t— 


XJ CTl 


CTl 


O CTi 



o 
o 
o 

i— o 



II 



4-> 

D_ 
<U 

Q 

S- 
CU 

+-> 

r0 



s~ 
<u 

o 



o 
ro 
ro 



n 



o 
o 



n 



cn 

CO 

ro 






L-> U 



ro 

LD 



CO 
LO 



CO 
CO 



O 



O 
O 
CM 



CU LO 

o o 





CU 


II 


> 




o 




jQ S_ 




<c o 


T 


o 

C r— 


3 


O Ll_ 


L-, 


■M C 




fO (O 




> CU 




O) U 




r— O 



139 



Table 4.2 

Estimated Linear Hydraulic Damping Ratios 
for Towers A, B, C, and D 







Towe 


rs 




Mode 


A 


B 


C 


D 


1 


0.00587 


0.00632 


0.01178 


0.01015 


2 


0.00251 


0.00304 


0.00576 


0.00541 


3 


0.00145 


0.00168 


0.00315 


0.00328 


4 


0.00107 


0.00126 


0.00246 


0.00233 


5 


0.00085 


0.00115 


0.00199 


0.00183 



Table 4.3 

Contributions of Each Mode to the Maximum 
Base Shear. ZABS Modal Combination 





Contri 


bution 


(as 


% of 


Total ) of Mode 


Tower 


1 


2 




3 


4 5 


A 


32.8 


40.2 




18.7 


6.8 1.5 


B 


33.0 


28.3 




24.0 


13.6 1.1 


C 


19.3 


24.6 




15.6 


35.0 5.5 


D 


38.9 


41.8 




17.9 


1.4 0.0 



Table 4.4 

Properties of System 4M, Mid-Frequency Range. 
3 = .02 in Each Mode 



140 



[K]: 



[C s ]: 



.00457 



3 lb-sec /in 



00457 .00914 .01371 lb-sec 2 /in. 2 



15.32 


-15.32 













-15.32 


45.96 


-30.64 














61.29 


-30.64 





lb/in. 




Sym. 




61.29 


-30.64 
76.61 




0.13917 


-0.06907 


-0.01734 


-0.01149 


-0.00479 






0.24264 


-0.09762 


-0.02638 


-0.00830 








0.28693 


-0.10783 


-0.01633 


lb-sec/in 




Sym. 




0.40007 


-0.12933 
0.58443 





Modal Properties 



de 


Frequency 
(cps) 


e n 


(estimated) 
(none) 


Hydrodynamic Parameter 
Participation Factor 
(none) 


1 


0.24705 




0.00794 


2.49115 


2 


0.55706 




0.00352 


1.13695 


3 


0.84337 




0.00233 


0.66289 


4 


1.06231 




0.00185 


0.25179 


5 


1.52207 




0.00129 


0.01573 



Table 4.4 (Continued) 



141 



Spectral Response Quantities (True Spectra) 



Mode 



'^'max 
(in.) 

12.618 
13.382 
9.316 
10.376 
10.811 



<|q| > 

(in.) 

4.044 
3.197 
3.096 
2.926 
2.712 



16.648 
22.807 
25.950 
38.248 
31.994 



<|q|> 



1 n 'max 
(in. /sec) (in. /sec) 



5.295 
7.056 
10.182 
9.798 
9.387 



142 



Table 4.5 

Hydrodynamic Parameters for System 4M. 
El Centro Earthquake 



Response 
Quantity 


Node 


Exact 
Value 


Modal 
Using True 

ZABS 


Superposition - 
1 Spectral Response 

SRSS 




1 


17.82343 


31.32392 


21.00747 




2 


16.05878 


21.29961 


16.04786 


{|x | } 
s max 


3 


13.26795 


18.78246 


13.53510 


(inches) 


4 


11.71001 


17.13259 


11.14007 




5 


10.23945 


11.85761 


6.68999 




1 


5.09378 


9.28465 


6.43887 




2 


4.08737 


6.63971 


5.12691 


(<|x |>} 
s 


3 


3.44525 


5.81354 


4.30800 


(inches) 


4 


2.63410 


4.96109 


3.32816 




5 


1.45048 


3.42885 


1.91468 




1 


31.62296 


50.63429 


30.31177 




2 


22.94491 


35.58812 


22.48838 


C|x 1 } 

s max 


3 


17.93618 


30.87149 


19.23872 


(in. /sec) 


4 


19.32336 


26.62459 


16.66792 




5 


13.95569 


22.63737 


12.06787 




1 


8.98920 


16.32071 


9.69329 




2 


6.82424 


11.41066 


7.21779 


{<|x s l» 


3 


5.89449 


10.20436 


6.32494 


(in. /sec) 


4 


4.96801 


8.89230 


5.18860 




5 


4.10293 


7.49280 


4.08744 



143 




WVWV v 



VVVWW 



\\V\\\\\ 



O) 




S- 




Z3 




+-> 




o 




3 




S- 




+■> 




CO 


r— 




Ol 


4- 


XI 


O 


£ 


r— 




CD 


s- 


-a 


(U 


o 


-M 


s: 


O) 




E 


j- 


03 


<D 


S- 


■»-> 


fO 


<D 


Q_ 


E 




fO 


-o 


s- 


<u 


rtJ 


Q. 


CI- 


E 




3 


TS 


_l 


o> 




D. 


-a 


E 


c 


3 


n3 


_l 






O) 




S- 


* — ^ 


=> 


-Q 


+J 


■ — <• 


o 




3 




s_ 




+-> 




co 




<u 




s- 




o 



CO 




to 
en 
a» 



en 

O 

s- 



c 
> 

Q 
co 

cu 





rtJ 




O 




■i— 




Q. 




,>^ 




h- 


oj 




s- 


4- 


3 


O 


4-» 




O 


E 


3 


<« 


S- 


£_ 


4-> 


en 


CO 


«o 




•^ 


<D 


o 


S- 




o 


a 


-C 


•r - 


CO 


+J 


4- 


fO 


4- 


F 


O 


CD 




-C 


^~ 


o 


(T3 


co 


O 




•i — 




Q. 


■-; 



'-^ en 

(13 •!- 



144 




o 
o 



o 
o 



o 

o 



o 
in 



o 
o 



o 

CM 



CM 
O 



o 

CD 



d) 

o- 

.c 
+-> 

S- 
<T3 



o 




o 


o 




i- 


• 




+-> 


o 




e 






o 


o 
o 




UJ 


LO 




o 

ti- 
ns 

S- 


o 




+-> 


o 




0) 


CM 


CO 


CO- 




Q_ 


CO 




o 


a; 


< ) 


* 


to 


o 


>- 
o 

liJ 


E 
O 
Q. 




^3 


00 




o 


a» 


o 


UJ 


Q£ 


in 


cr 






u. 


E 


o 




o 
+-> 

n3 

E 
S- 


o 




o 


CM 




M- 


• 




<U 


o 




O 
O 


o 




-t-> 


— -• 




CO 


o 




UJ 


m 

CD 




C\J 



Q> 



o 
o 



o 

LP 



D 
CM 



O 
O 



o 



o 

CM 



in 
o 



CM 

■ 



33S/NI 'UI3CTGA 



145 




o 

UJ 

en 
en 

UJ 



— 'O 




COo 






en, • 




-t- 



-t- 



0.0 3.0 6.0 9.0 12.0 15.0 18.0 

TIME (SECONDS) 



21.0 



21.0 



27.0 



30.0 



Fig. 1.3 Ground Acceleration, Velocity, and Displacement of 
El Centro Earthquake, 1940, N-S Component 



146 




0.0 3.0 6.0 9.0 12.0 15.0 18.0 

TIME (SECONDS) 



21.0 



24.0 



27.0 



30.0 



Fig. 1.4 Ground Acceleration, Velocity, and Displacement of 
Taft Earthquake, 1952, N-21-E Component 



147 




0.0 3.0 6.0 9.0 12.0 15.0 18.0 

TIME (SECONDS) 



21.0 



24.0 



27.0 



30.0 



Fig. 1.5 Ground Acceleration, Velocity, and Displacement of 
Ferndale Earthquake, 1954, N-44-E Component 



148 



CEO 

CO 

UJ 



UO 





en 

Ujw - 
C_> 



UJO 

2: 



d 



CL. - 




0.0 2.0 4.0 6.0 8.0 10.0 12.0 

TIME (SECONDS) 



14.0 



16.0 



18.0 



20.0 



Fig. 1.6 Ground Acceleration, Velocity, and Displacement of San 
Fernando Earthquake (Pacoima Dam Record), 1971, 
S-16-E Component 



149 



c 




/ 


/N. 
















6r\ 

X\ 






X/ 




/ X^ / ■ 


<?x 


\f 


4/ \ 








/ \ 


y/\ 




/ \ 






y X. 


/v 


X X 


\ / 


x < 


X ^ 


\ / 




\ // x* 


ex 




xX 
/X 


l*X 














f^f 












/\ 






x; 


N^^ 








V 7 




xC $ 


%r 


X 

N 



0.01 F 

0.20 \/ 
n en . i 


3 \ 








a^/ 


/ \ 




. 11 11 n n ^ 

i>£ M s«£ ^£ . y 


\$>y 


y\ / 


/ \ 


x^ 


»\/ x^ 




XXX 

fO <o <o 
v E E E 

' Q) D) Ol 

:x :x :x :> 


fl3 ' \ 

E 

< / 






\/ 








1 




\t 1 




Q X 

- X 




X y/ \< 


^x 
7 N 






\/ 


1 1 


, N/ 


\/ 







8 



o 
o 



o 
o 



o 
o 



o 
in 



o 

o 



o 



o 
o 



o 
o 



in 



o 
o 



o 
o 

II 

CO 

CO. 



C\J 



o 

(LI 



C\J 

e 

CO 

l£> 








,_ 









cv 


CO 

Q_ 


II 




O 


c 
:x 






>- 


i- 




(_> 





— ' 


2 
LU 


<+- 




zd 


ro 







S- 





LU 


+-> 


in 


CC 


a 


• 


U_ 


a> 







Q. 
CO 

a> 

CO 

c 










<\j 




Q. 


O 




CO 


O 




E 
O 


« 




-f— 







A3 

E 
S- 


in 




O 







«t- 


. 




CU 







Q 

O 

•U 
CO 


cu 




(0 



01 



CNJ 



O 
O 



CNJ 



8 



o 

Ln 



D 



in 



CNJ 



03S/NI 4 UI0Q~GA 



150 



o 
o 




o 
o 

II 
«/ 

CO. 



CM 



o 

to 
+J 

4- 



+-> 
CM 

c 

•r- 

00 



en 



:x 

s_ 
o 

<T3 

i_ 
+J 
O 
OJ 
Q. 

oo 

<L» 
CO 

c 
o 

Q. 

to 

q: 

e 
o 

+J 

OS 

E 

s- 
o 

4- 

O) 



-M 

to 

<T3 



CM 
CM 



33S/NI 'UI3CTGA 



151 








o 


o 




• 


o 




o 


• 




II 


o 




1 


-~" 




CO. 


o 






o 




-o 


o 

LO 




o 
o 

(1) 


r» 




c 


o 




o 


. 




•n" 


o 




+-> 


C\J 




S- 


o 




^~ 


o 




<D 


« 




U 


o 




o 






< 


o 
o 




OQ 


lo 






o 




00 


o 




E 


<\i 


GO 


S- 




Q_ 


<u 




o 


1— 


r> 


. 


X 


n 


>- 






CJ 


CO 


^i 


z 




n 


UJ 
ZD 

o 

UJ 


o 
<*- 


LO 


IT. 


fO 


o 




s. 
+-> 
o 

O) 
Q. 
CO 


o 






C\J 




CD 



o 
o 



LO 

o 



o 






o 


D 


O 


. 


■ 


o 


D 


O 


o 


D 


LO 


C\J 


••« 


in 


rj 



LO 



(V 



C 

o 

Q. 
</) 

OJ 

ct 

c 
o 

+-> 

(O 

E 

i- 
o 
**- 

O) 
Q 



to 
(0 



CO 

cvj 



33S/NI *UI3Q"GA 



152 








in 






o 


o 




• 


o 




o 


o 




II 


o 




( 


""* 




QQ. 


o 






o 




-o 


o 
in 




o 
o 


o 
o 




c 
o 


n 




-l-> 


CM 






o 




^~ 


o 




<L> 






o 


d 




u 






a; 

V) 


o 




03 


o 




CQ 


in 




10 

•i— 

$- 


o 




oo 


o 




E 


rw 


co 


s_ 




Q_ 


cu 




o 


1— 


r> 


* 


X 


r> 


>- 


•r* 




(_) 


C/> 


__, 


2 






UJ 


S- 




ZD 


o 




o 


ti- 


n 


UJ 




in 
d 


cc 


ro 
S. 

4-> 
O 
CD 
Q. 

(/> 


o 

C\J 




V) 


o 




c 
o 

Q. 


o 




<D 


■•— < 




C£ 



CO 



«o 

E 

S- 

o 

Q 
U 



in 

fO 



«3- 
en 



03S/NI 'UIOCTGA 



153 



o 
o 




CO 

Q- 
O 



CJ 

UJ 
ZD 

o 

UJ 

cc 
u. 



(0 

i- 

•4-> 

U 

O) 

Q. O 
CO O 

O) 
CO II 

c 

O 00 

Q_ CO. 

to 

<u 
c£ • 

<L> 

o <o 

•r- 3 

-!-> O" 

fC SZ 

E 4-> 

s- s- 

O n3 

q- lu 
a; 
Q o 

S- 
O 4-> 
1- C 
+-> <D 
co O 
(0 



CVJ 

C7> 



33S/NI 'UIDCTGA 



154 



o 
o 




CO 
Q_ 
CJ 



O 

UJ 

ID 
O 
UJ 



s- 
o 

<D 

Q-CNJ 
00 o 

CD 
W || 

c 

O V) 

Q-ai 

o 

at 

ai 

O ro 

•"- 3 
■M O- 

<a .c 

E 4J 

s- s- 

O fO 
M- UJ 

CD 

Q O 
S_ 

<-> -M 

5g 

</> <_) 

<T5 



CM 

cn 



03S/NI 'JL1I3013A 



155 



o 
o 




CO 

o 



u 

UJ 

o 

UJ 



S- 

o 

CD 

Q.LO 
CO o 

CD 
l/> || 

c 

O (A 

Q-OQ. 

(/) 

O) 

cc . 

<u 

c .* 

O ro 

1- 3 

■<-> o- 

rt3 JZ 
E 4-> 

s- s- 

O fO 
l|_ uj 

<u 

Q O 

s- 

O +J 
•r- C 

+J 0) 
(/) o 



CM 

en 



33S/NI 'X1I3013A 



156 



o 
o 




to 
o_ 
o 



UJ 



en 
ro 

s_ 

Q 

S- O 
rO CM 

OJ . 

c o 

r— II 

e 
o ^ 

X 

"0 CO 
C E 
(O 

CO 

s- :x 

ro O 

O) ^ 

c 



o 

+J O 



ro to 

S- CQ 

U 

«D • 
Q. <D 
(/> O 

c 

CU ro - 
to jQ 

C S- 
O 3 
GL4-> 
lO I/) 

CU ••— 

or q 



o 
in 

o 


^3 

o 

UJ 

cc 

Li- 


ef ormati on 
on of Base 


o 

CM 




+-> 

U ro 


O 




asti 
sent 


r> 




r— CU 






UJ S_ 


■ 




Q. 


o 




<4_ CU 
O CC 


UJ 

O 




O CU 

tO 'r- 


o 




ompari 
or Ser 


CM 




t_> 4- 


o 






o 




00 
CVJ 


•— * 




. 


o 




co 


■ 




'r- 


o 




U_ 



o 


o 


o 


a 


i 


o 


D 


o 


o 


o 


LO 


CM 


■— • 


LD 


CM 



if) 



CM 



33S/NI 'UIOCTGA 



157 



y^ 
























/^ 


'\/ 






^c/J 








\ / 






CT1 


z 









































\ c 
i 


L 

>- 
V 

5 


Linear Drag 
(Eq. 2.5) 

\ /I \/ 


\# 




y \ 


X^ 


XX' • / 






r- 
v ! 

/* - 


















, /°h 






: \ 


















X < 


b* 














\*>/ 








v / 










: / 
: \ 






^v ' 












// N, 


\ 














/\ /< 










N 


: / 
















/ \ 
















<3 


























\V 


























/^\ 
<? 


\/ >v 




















s. / 


















\ / 






^ 


V / 






\/ \i 


7 \ 














, / 












i / \ 












6^/ 


















x\ 








\ < 


s\. 




















/ 


\/ 
















\ / \? 


7 \ 








\/ 




\/ 






\y 



o 
o 

• 

o 
o 



o 
o 

• 

o 
in 



o 
o 

o 



o 
o 



— o 



o 
o 



Ol 




(0 




s_ 




Q 




S- 


o 


03 


CM 


CD 


• 


c 


o 


•^ 




^~ 


II 


C 




o 


:*£ 


z 


"» — 




X 


■o 


«o 


c 


E 


(O 






o> 


s_ 


:x 


fO 


Q 


CD 


^ 


c 




*r~ 


a 


_l 


in 




o 



+-> o 



UJ 




(T3 to 






s_ en. 






4-> 






O 






CD • 






Q. CD 


O 




CO o 

c 


cv 


CO 

Q_ 


CD (0 
CO XD 




o 


O 3 


n 


* 


Ql4-> 


n 


>- 


CO CO 




o 


CD T- 


— ■ 


2 
UJ 


q: q 




3 


c o> 




o 


O to 


o 


UJ 


•i- fO 


LP 


cc 


+J CO 


• 


u. 


<o 


o 




Deform 
ion of 


o 




+j 


<\J 




O fO 


o 




asti 
sent 


o 




r— CD 






UJ S- 


. 




Cl 


o 




4- Ol 

o q: 

C CO 


LO 




o a> 


o 




CO •!- 


* 




•i- s_ 


o 




Compar 
for Se 


l\J 






o 






o 




CM 



cn 



o 


D 


O 


. 


. 


o 


D 


O 


O 


D 


LO 


(M 


«-< 


en 


f\J 



(V 



33S/NI 'UIOCTOA 



158 



o 
o 




$- 
Q 

S_ 

O) 

c 



-a 




E 




fO 




S- 




cC 




O) 




c 




•^ 




_J 




-C o 


4-> Lf> 


•r~ 


• 


3 O 


rC 


II 


s_ 




+-> 


^ 


o 


*»^, 


CD 


X 


a. 


ra 


oo 


E 


a; 


a> 


co 


:x 


c 


Q 


o 


^ 


Q. 




10 


fl 


0) C\J 


a: o 


c 


O 


o 




•^ 


II 


■!-> 




rC 


CO 


E 


CO. 


S- 




O 




4- 


• 


d) 


O) 


a 


-^ 




ra 


CJ 


3 


•r— 


O" 


-»-> 


.c 


CO 


-M 


<o 


£_ 


r- 


fO 


LU 


LU 


4- 


O 


O 


S- 




4-> 


c 


C 


o 


<U 


to 


O 


•^ 




s_ 


^~ 


fO UJ 


Q. 




E 


s- 


O 


o 


O 4- 



CVJ 

C7> 



33S/NI 'UIDCT13A 



159 



-*■ 



/ ? 



> s 



\ 



i 



/ 



co 
o 
o 



00 

o 



o 
id 



i 

\ 






<n 

E 


X 

E 


:x 


i^ CD 

:x 


Q 






o 



o 

CXJ 



o 
o 



ID to 
CL 



>> 

o 



CNJ 



oo 
o 



CO 

o 



«3- 
o 



6eug jeauL[U0N * |z 

c , xeui, i 
6euQ ueaun * z 



T3 o 
<u o 

N • 

Z. n 

CD CO 

e ca 



0) 

.^ 

• fO 

E 3 

o cr 

•i— -E 
4-> +-> 

3 s- 
■— fO 

O LlJ 

oo 
o 

(O +-> 

cd e 

E CD 
•r- C_> 



O LU 





E 


"O 




CD 


E' — 


o 


3 


fO >> 




o- 


4-> 


CM 


cu 


S_ T- 




s_ 


fo a 




Li_ 


Line 
Velo 


o 










4- S_ 






O O 
+J 
E fO 
O r— 
CO l — 


ID 




s- o 






fO CO 


O 




11 Comp 
by 


C\J 




CXJ 


O 




CD 



160 























. • • * 












# • * " 






















m 


• • 










, • " 












# " 




























^ 










«' 










.•» 






















^^ 










# • • * 


^» ^ 












/ 




/ 






• • 


/ 




/ 








f 


j 


r 






• 


S 


y 








y 




s 








•• 




_0— 








• • 




^^^^^ 








• 












• 












• 


^^^^^ 










\ 


^^^ 










\ 


«r 






\ -^ 


VC 


> 

? CO c 










c 


3 








o o ir> 






S K \ 


• 






/ / 


O o o 






/ ' : 








( ' ' 


II II II 






\ \ . 








N \ • 


X 


X 


X 








^-- * 


(0 

E 


E 


E 








****«^ 
















CT 


^ en 


^ CT 


^ 






:x 


:x 

o 


:x 








/I 


Q 








(\ 


5*i 


^ 


1^ 








\ 












\ 


' 


1 i 










* 

1 




L 





o 



o 

CM 



o 
o 



in tn 

Q_ 

o 



>» 
a 
c 
a> 

o 3 
• cr 

cm a> 



IT) 

o 



CM 

o 



•o 
ai 

N 
•^ 
J- CM 

<a o 

a> • 

c 

T- II 



QQ 



o a> 

•r- ^Z 

+-> fO 

i— O" 
O -E 

l/> 4-> 
S- 
S- fO 
03 LU 
CD 
E O 

•r- £_ 

i— -M 
E E 

o a> 

z o 

-o •— 

E UJ 
(0 >> 

ai +J 

E t- 

1- o 
_l o 

<+- 'a! 



e s- 
o o 

to 4-> 

•r- (O 
J- i— 
fO i— 
Q.-I- 
E O 
O </> 

o o 



CM 
CM 

CO 



CM 



CO 
O 



o 



o 



6eug ae9UL[U0N <xeiu lz 
6eua ueaun ' XBUJ |z| 



161 



y 



• \ 




L 



to 

o 
o 



00 

o 



o 

Lf) 



:x 






cn^ 



:x 






CD^: 




o 



o 
c\j 



o 
o 



in c/> 

Q_ 

o 



>> 
o 

c 
<u 

O 3 

• Or 

CO 0) 

S- 



o 



C\J 

o 



<\j 



oo 
o 



O 



o 



-a 

0) 

rg tn 
•i- o 

s- • 

ra 

ai ii 

c 

•r- to 

_i en 



cu 
. -* 

O =3 

•i- cr 
+-> .c 

Z3 4-> 

i— s_ 

O fC 
OO LlJ 

s- o 

c e 
•i- cu 
r— C_> 
C 
O r— 



c -— - 
fO >> 

i- 'I- 

03 O 
<D O 

C r— 
•r- d) 



o o 

4J 
C <TJ 
O ■— 
tO i — 

i- O 

fO to 
Q-O 
E 

O >> 
O -Q 



CO 
CM 
CD 



6eug up9ul[uon ' Jz_ 
6eua uesun tXBlu |z| 



162 















10 

o 
o 

• 

o 
II 


00 

o 

• 

o 

II 


= 0.50 

1 








J 






X 




X 




X 










'i 






m 




id 




ro 










.P 






E 




E 




E 
















a 


i^ 


:x 


:x — 








H 






:x 








/' J 






Q 




Q 




Q 










/ '] 






^ 




iZ 




^ 










' •'" 










































t 


/ 




















I 


/ 














1 - 






• 


/ 












• 


/ 1 




















• 


1 
















." 


1 


















• • 


1 
1 


















— -^ .. 


/ 1 A 




















/ 


CD 


















* 




• X 


A 
















s 







C\J C7> 
















s 




<\J C31 


•X 
















SJ- \ 




•X 


V 
















x^. \ 


i 




















\ ' 


















I. 


1 


















/•' 


/ 


















/•' ' 


1 


















Vi^. »i 






















^j 




















1 


















I 































o 
o 



o 

o 



o 
o 

o 

LD 



O 
O 



o 

C\J 



o 
o 



_ o 



o 
o 



o 
o 



CM 



o 
o 



o 

LP 



o 



o 
o 



LO 

o 



cu 
o 






O 



o 

c 

QJ 

cr 

a> 



E 
O 
T3 
Q) 

a> 
s_ 

u_ o 
o 

o 

II 

s- ca 

en 

<U 

Q . 

«u 

at -*: 

i— (O 

en =» 
c cr 

•r- .c 
co +j 

s- 

S- fO 
O UJ 

<+- 
o 

S- S- 

<U 4-> 

+J c 

CD <U 

E O 
<T3 

S- r— 

03 UJ 



CT) 



o 

fO 



o 

10 

o 



I — 

. 
C\J 

en 
lZ 



O 
o 



o 

in 



o 



o 






o 



Lfl 
CD 



c\j 
o 



D9S/'UL ■ 



<> 



<| S x|'x> 

• 6* 



163 









1 






























y£> 






















o 


00 


O 


















o 


o 


Lf> 


















• 


• 


• 


















o 


o 


o 












ill 








n 


1 


II 




















X 


X 




X 






















<o 


(0 




«o 






















E 




E 




E 












































:x 




:x 




:x 














f,l 






a 




o 




Q 












f ; 










s*£ 




S*i 




:*; 












1 l ' 


























: l 


























.' 1 


























1 1 






















.* 


/ 
























• 


/ 
























• 


/ 
























. 


/ 


















• 




J | 






















\ ' 




















>k •, 


1 


A. 




















*^ -1 


1 
/ 


X 


A. 
CVI o> 






















\J C7> 


•X 


















•' / 




< 


V 
















^^. • 


•X 


















>/. 


\ 


1 , V 




















*iz» % 


h 






















^o 


• N 
























\: i 
























1 ' 
























r-'i 
























1 l 






















Ss ^>. 
























^>^ 













































































o 






o 






o 






o 






~* 






o 






o 






o 






LO 






o 






o 






o 






OJ 




E 
o 


o 




a> 


o 




a> 


o 




U_ C\J 






o 

4- • 

o 


o 
o 




II 
a> 


in 




a> 

Q • 


r> 




r- (O 


o 




C7> 3 






c cr 


C\J 








to 


S_ <T3 


o 


a_ 


O LU 


o 


(_> 


4- 


• 




o 


*—• 


A 


S- J- 




>> 


a> 4-> 




O 


4-> C 


o 

Lf) 


c 


<D a> 


<u 


E O 




zs 


rc* 


o 


er 


S- i— 




<u 


to UJ 




£_ 


Q_ 




Li- 


C7> • 


n 




i- o 


<\i 




N +-> 






•i- fO 


O 




near 
cill 


O 




T- (/l 


• — 




_J O 


o 




IT) 


LO 

o 




CVJ 



o 






o 
o 



o 

LO 



o 



d 



o 
Ln 



D3S/'UL 



o 




o 


• 




• 


C\J 




*"" 


( 




<> 




< 


S ,S 
X X> 

• 2* 



in 
o 



« 



o> 



164 





































o 


00 


o 














o 


o 


in 












• 


• 


• 
















o 


o 


o 








:l 
d 








II 


II 


II 








•| 








X 




X 




X 












1 






re 




re 




re 










:i 






• E 




E 




E 










;i 








cn:*: 


cri 


i^ 


cn^i 
















:x 




:x 




:x 










:l 








Q 




o 




Q 










);\ 








«M* 




^ 




i*£ 










/»' 






















1 • ' 
























/ ' ' 
























/ . / 
























.' / 






















/ 


/ 1 






















/ 
























1 






















l 


















^^w*. 


l I 




















I 


A 




















*"/ 


Ol 


A 
















1 * 


/ 


• X 


CVJ Cn 
















^^?' 


r~ 


c\j en 


• X 

V 
















\ x 


1 V 


















\ 


^ 






















»^ 






















^S» x 






















^SN 






















>/ 






















A* 




















v^ 




















^*^_ 


1 















o 
o 



o 
o 



o 
o 

o 



o 
o 



o 



o 

o 



- o 



o 
o 



o 
o 



C\J 



o 
o 



o 



o 

C\J 



o 
o 



in 
o 



CD 



CD 

o 



oo 

Q_ 

o 



o 

c 

<u 

i- 



o 
-a 
<u 

<D 

s- 

u_ in 
o 
«♦- • 
o 

ii 
01 
a> to 

cn 
0) 

Q . 
01 

O) -^ 

r— re 

Cn =J 

c cr 

•i- -C 
GO +J 

s_ 
s_ re 

o UJ 

o 

S- i. 
O) -M 
4-> C 

O) CD 
E O 
re 

i- r— 

re uj 
a. 

en • 

c &- 
■i- o 
N +-> 

■r- re 

i. I— 
re i— 

<U ■r- 

c o 

•r- to 
-J o 



t£> 



CVJ 



en 



o 
o 



o 

LO 



o 



o 
d 



o 

in 



o 

C\J 



Lfl 

o 



C\J 

o 



oas/'uj. * 



<> 



,s ,s 



165 



o 
o 




CO 
Q- 
O 



(_) 

-z. 

UJ 

o 

UJ 

cr. 



■o 




O) UD 


N 


o 


•^ 


o 


S- 


• 


*o 


o 


CD 




c 


II 


•r- 




_1 


iz 




X 


E 


fO 


3 


E 


s_ 




-t-> 


cn 


o 


:x 


o> 


Q 


Q-i^ 


CO 






n 


CD CM 


ro O 


S- 


• 


Q O 


S- 


II 


<o 




01 


l/> 


c 


CO. 


■1— 




_l 




.c 


0) 


-(-> -* 


•^ 


<o 


3 


3 




CT 


F 


-C 


3 


+-> 


S- 


s_ 


+J 


<0 


O 


UJ 


01 




Q- O 


CO 


S- 




+J 


cn 


c: 


«o 


<D 


i- O 


Q 






^— 


S- 


UJ 


<T3 




<D 




C 


• 


•r— 


*»■■** 


I— 


>> 


c 


■4-> 


o 


•^ 


z: 


U 




O 


*4- 


^~ 


O 


a> 




> 


c 




o -o 


</> 


£ 


•r— 


3 


i- 


O 


(O 


S- 


Q.CJ3 


E 




O 


>> 


o -a 


r^. 




n- 




• 




CM 





cn 



33S/NI 'JL1I30H3A 



166 



o 
o 

d 




o 


at 


o 

LP 


N 00 
•r- O 
S- • 




fO o 




CD 




C II 


O 
O 


Ij ^: 



o 

O 
UJ 

cr. 



X 



en 
x 

Q 



S- 
+-> 
O 
CD 

CO 

Cne\J 
rtJ O 
i. • 
Q O 

i- II 

<1> CO 

C QQ. 



-C CU 
CO 4-> J* 

0_ 1- n3 
CJ 3 3 

cr 



s- s- 

+-> (O 

U LU 

(U 

Q. O 

co s- 

4-> 

en c 
to <u 
s_ o 

Q 

S- UJ 

(0 

<L> 

£Z • 
•r— *~~"» 
>— >> 

C +J 

O -r- 

Z U 

O 

<4- i— 

O <D 
> 

c 

O t3 
CO C 
•r- 3 
S- O 

m s- 

Q.O 
E 

o >> 
O -O 



00 



C\J 



en 



. 


o 


o 


o 






o 


■ 






o 


o 


o 


o 


o 


d 






— ■ 


LP 


C\J 


~* 


LP 


r\j 



Lfl 

d 






33S/NI 'UIOO~13A 



167 



o 
o 




en 
o 



>- 

UJ 

o 

UJ 

cc 



-a 
cu 

n o 
•r- in 

S- • 

<T3 O 
OJ 



X 

E <0 
=3 E 
$_ 

+-> o> 
o :x 

<D O 
CDCVJ 

(O o 

i- . 

Q O 
S- II 

to 

OJ </> 



1- ro 






3 
S- 
-(-> 

u uj 
a> 

Q- O 

+J 

CD C 
03 <D 
S- o 

S- LU 

<a 
a> 
c • 

^ >> 

O 'I- 

z o 
o 

o <u 



O X3 
V) c 

•i— 3 
i- O 
fO i- 
CLC3 
E 
O >> 

O -O 



cr> 

CM 

CD 



■ 


o 


D 


O 






o 


• 






o 


O 


o 


o 


D 


d 


• 


• 


—- ■ 


m 


(\j 


w-» 


lh 


ra 



1/7 

d 






D3S/NI 'JL1I3013A 



168 













0.006" 
0.08 

0.50 














ii n n 




\ 

N 

\ 

S 








^ ^ ^ 

XXX 

E E E 

CD CD CD 

:x :x :x . 






"S'-^' — 




- — •—.-» 


Q O Q 
i<£ :*£ :*£ 




- — — —"" 


1 

1 
1 
1 










""••., 


... 


— — 


~""^ v v 














1 „ 


X 
V 










\ * " * 


■ . . . 












* 










. *-J * ** * 


■ . > 

1 # .j> 


\ 
•N 










' m ^sl^ 


!**> 




-* "** 











o 

LO 



o 




CD CVJ 


o 




N O 


C\J 




i_ O 

CD II 

C 


o 




f- to 

_l CO. 


o 




' 






ution 
uake. 


o 




r— cr 




O -C 


in 


in 


CO +-> 




o. 


S- 




o 


re LU 




m 


CD 




>» 
o 


C O 
•i- S_ 




c 


i— +J 




CO 


c c 


<— > 


3 


O <JJ 




cr 


2: o 


C\J 


CD 






i_ 


"O i — 




U_ 


C LU 

re 


<— > 




fO' — . 






a> >> 


i™ - 




of Lin 
elocit 


in 




> 






c 


O 




ompariso 
y Ground 


CVJ 




O -Q 


o 




o 

CVJ 



C\J 



CD 



CVJ 



O 



CO 

o 



LO 

o 



«3- 
o 



CVJ 

o 



66JQ JB9UH - 



XBUli 



Z| ul uoL^onpecj 



6buq ueauLLUON - z 



UL U0L^Dnp9cJ 



169 



100.0 



50.0 



20.0 



10.0 



5.0 



B 2.0 



1.0 



0.5 



0.2 



0.1 









^\. 










N / 


4 / 




\/ 


\J 






















A 


/ 










Z~i — -\ 


N">< 






\ / 












y /\ 




\.T 






\\\V 






A 

\ / 


V 




\a// 




















\ / 










\ / 








\ V 




\ / 


N v^ 






*> > 










\ ^ 


N/ ' 




\ / 








/X* 


















\ / 




' \ 


\ / 




\ / 












S / 



0.01 0.02 



0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 



< a ) 6 S = 0% 6 h = 0, 1, 2, 5, 102 



100.0 



50. 



20.0 



10.0 



5.0 



o 2.0 



1.0 



0.5 



0.2 



0.1 



N v' 






r\ 












^ / 






v 




/\ 














/^ 






\ / 








' \ / 


vr^"/ 


s"^y 


Vvjix 




\ / 




\ / 


N v' 




x If' 


7 / ) 




\.¥ 












\/ 














/^V 










A 










y/^i 


\ / 


\ / 






x 3 




\ / 


N v' 






X- / 










\ ^ 


'v' ' 






v 






"%> 


y \j 
















\ / 










\ / 


\ / 


\. S 


\ / 









0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 
( b ) 6 S - 2% B h = 0, 1, 2, 5, 10% 



Fig. 2.21 Elastic Deformation Response Spectra for El Centro Earthquake 



170 



100.0 



50.0 



20.0 



10.0 



5.0 



o 2.0 



1.0 



0.5 



0.2 



0.1 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 



(°) 6 S = 5% 6 h = 0, 1, 2, 5, 10* 



100.0 



50.0 



20.0 



10.0 



5.0 



B 2.0 



1.0 



0.5 



0.2 



0.1 









V\ 












4? / 






v 








J&/1 










"% 






/ < 






\A 


$%sy\ 






\/^h 


N v' 






\ / 












\*Y 


XA,/ 
























~>&> 


s\. N 












K / /^ 






v^& 






ssy\ 

\7 \y 
















X- ? 










\ <$? 


V 












yfo 


















\ / 










\ / 


\ / 


^\. s 


\ / 




8^/ \> 





0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 

(d) 6 S =10% 6 h = 0, 1, 2, 5, 10X 



Fig. 2.21 (Continued) 



171 



100.0 



so.o 



20.0 



10.0 



5.0 



S 2.0 



1.0 



0.5 



0.2 



0.1 









v\ 












<p y 






V 








j^/ 
















/* 








$y\~, 














s / 


\ ' 








X yf/-^ 


\~iv 


^b/ 












A 

v 






ur 






















•X 






\ / 




$y X/ 








S > 




/ ' X 




Xo., / 










\ ^ 






v 






x? 




X 










N X/' 


/ X 




><^ 




N / 




\ / 


\ / 




N / 


\ / 





0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 

B. = 0, 1, 2, 5, 10% 



(a) 6 S = 0% 



100.0 



50.0 



20.0 



10.0 



5.0 



o 2.0 



1.0 



0.5 



0.2 



0.1 





















\? / 


// \ 












\&>/ 










/x 








i(\ 






^rX 






AX% 


N / 






\ / 


N v' 








v ///9 


\~r 


X^j~X 
























/^" 


c§A 1 










\ / 










N / 




\y X^ 


\ / s 


>\A 




\ / 


















\ ^ 








V 






y(o 














A\ 


\/ 




xlk 


• x 






\ / 















0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 
(b) 6 S = 2% 6 h = 0, 1, 2, 5, 10% 



Fig. 2.22 Elastic Deformation Response Spectra for Taft Earthquake 



172 



100.0 



50.0 



20.0 



10.0 



5.0 



K 2.0 



1.0 



0.5 



0.2 



0.1 









^\ 












4 / 














J&/ 












\df 


A 








\ / 


^v 












\ / 





\s 










\\~3r 


V^T/ 


N>T\ 






\ / 


A 














"0\ vWN 






\ ' 




\ / 










\ / 








v 




















\ ^ 


/ ^ 




a 






/ 


y& 




/ 


v 




\/ 


/ \ 






/ 
S / 






\ / 




\ / 


A,. 


K> 




< A/ 


c> 



0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 



(c) 6 S = 5% 6 h = 0, 1, 2, 5, 10% 



100.0 



50.0 



20.0 



10.0 



5.0 



o 2.0 



1.0 



0.5 



0.2 



0.1 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 



(d) 6 S = 10% 



= 0, 1, 2, 5, 10% 



Fig. 2.22 (Continued) 



100.0 



50.0 



20.0 



10.0 



5.0 



o 2.0 



1.0 



0.5 



0.2 



0.1 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 
(a) S s = 0% 6 h = 0, 1, 2, 5, 10% 



100.0 



50.0 



20.0 



10.0 



5.0 



o 2.0 



1.0 



0.5 



0.2 



0.1 









v\ 






A 






4 / 




















\ / 








/ \ 










%w\ 


\x 






\ / 


\ y 












\y? 




\.^ 






\/ 










\/4 


1// 








/x 










N / 


\ / 


w ' X/ 






Y^& 




\ / 








y 


\ / 


\ / 






4> ? 










\ ^x 




\\ / 










^(o 




/ \ 














\ / 


Y% 




\ / 




\ / 




\/ 


\ / 






\ / 



0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 
(b) 6 S = 2% 6 h = 0, 1, 2, 5, 10% 



Fig. 2.23 Elastic Deformation Response Spectra for Ferndale Earthquake 



100.0 



50.0 



20.0 



10.0 



5.0 



S 2.0 



1.0 



0.5 



0.2 



0.1 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 



(c) 6 S = 5% S h = 0, 1, 2, 5, 10% 



100.0 



50.0 



20.0 



10.0 



5.0 



o 2.0 



1.0 



0.5 



0.2 



0.1 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY, CPS 

(d) b s = io% a h = 0, 1, 2, 5, 10* 



Fig. 2.23 (Continued) 



1000. 



500. 



200. 



100. 



50. 



o 20. 



10. 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY, CPS 
(a) 6 S = 0% 6 h = 0, 1, 2, 5, 10% 



1000. 



500. 



200. 



100. 



SO. 



o 20. 



10. 



5. 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 



(b) 6 S = 2% 



0, 1, 2, 5, 10% 



Fig. 2.24 Elastic Deformation Response Spectra for San Fernando Earthquake 



1000. 



500. 



200. 



100. 



50. 



176 



S 20. 
d 



10. 



5. 



2. 







N.f/ 


r\ 












£, y 






v 
























/) 






\ / 


X\ 






sh 




\ / 




\ / 


s s/ 






























^ml/ / / 








X^vv^^ 










\ / 






\ / 






N v^ 


afx 








\ / 


\ / 




^y^\ 


X- / 












\ v pi 






v 










\/ 








XN 


1 ^X 




A 

\ / 


x? 

xx 


\ / 


\ / 




\ / 


\ / 






N / 




N / 



0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 



(c) B s = 5% 



= 0, 1, 2, 5, 10% 



1000. 



500. 



200. 



100. 



SO. 



20. 



10. 



\ / 






v\ 












4? / 














«*/ 










XX. 






s / 








#y 


\ / 












\ / 














y p 












v 










v?L ^ 














/ /m^\^ 












X' 

/ x<? 
















\ / 




V X 














\ N ^^ 






v 


















X"\ 


M&\ 






XX 


\ / 






\ / 






\ / 


\ / 







0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

FREQUENCY. CPS 
(d) 6 S = 10% 6 h = 0, 1, 2, 5, 10% 



Fig. 2.24 (Continued) 



177 




o 
o 

d 
o 



o 
o 



o 



O 
O 



O 
OJ 



o 
o 



- o 



o 






<T3 

■»-> r>* 
o o 



o 




CO (0 






C -M 


LD 




ibutio 


O 




S- d) 


O 




co re 


CM 


CO 


•i- 3 




Q_ 


Q cr 




O 


o +> 


O 


>- 
CJ 


5 s- 

UJ 




LU 


S- 




ZD 


O CD 




a> 


<4- r— 


(-) 


LU 


rC 


LD 


<r 


rd -O 




u. 


S- E 


O 




Spect 
Fer 


o 




M- O 


c\j 




O -i- 


• 




+J 


o 




£Z r0 
O C£ 
CO 
•r- CD 


o 




i- c 


"""* 




ra »i- 


o 




Q. Q. 




E E 






O A3 






O Q 


LO 






o 






O 




LO 

CM 



CM 



o> 



o 
o 



o 
in 



D 
fAJ 



O 

d 



o 
in 



o 

fAJ 



in 
d 



r\j 



03S/NI 'JL1I3013A 



178 




00 
C_> 



o 

c 
<u 

cr 

s- 



E 

S_ 
-t-> 
U 

O) 
Q. 

oo 

O) 

to 

c 
o 

Q. 

(/> 

CD 
q; 

c 
o 



E 
s- 
o 

4- 

Q 

O 

■♦-> 
«/) 



T3 
CU 
N 






c 
o 

"r™ 
•4-> 

o 

S- 
+-> 
</) 

C 

o 
o 



C\J 



CM 
CD 



^LD0[9A 



179 



1000. Q 



soo.o 



200.0 



100.0 



•« 50.0 



20.0 



10.0 



5.0 



2.0 



1.0 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 

( a ) l*cL;,v 



100.0 



50.0 



20.0 



10.0 



5.0 



2.0 



1.0 



0.5 



0.2 



0.1 









v\ 












4 / 




\ / 


V 








J&X 










%> 


r <b<? A 




X 


** /*\ 


\ / 




$/\r? 














p z 


\ / 








'V/y \-i 
















A 




\//V 




/ / 








\/- 








\ / 






/ /\ 


^(% 


N v^ 






\ / 


K / 




\ / 




\ ' / 




4> y 










\ $ 








\> 






\xb 


















\ / 


X<9 








\ / 












\ / 



0.01 0.02 0.05 0.10 0.20 



0.50 1.00 2.00 
Frequency, CPS 

(b) <|x s l> 



5.00 10.00 20.00 50.00 100.00 



Fig. 2.27 Elastic Hydrodynamic Parameter Response Spectra. 
El Centro Earthquake. 3 total = 0, 1, 2, 5, 10% 



100.0 



50.0 



20.0 



10.0 



5.0 



2.0 



1.0 



0.5 



0.2 



0.1 























180 






\.#X / 


o 










4 / 




\ / 




X y* > 


















-p/ 

•ft. 




/ s! 








W\/ X 


■~ / 


\ ^"•■2 


\ - / 


\ / 


~£—-y 






\/ 






JyVA 


' /\ ^ 


max 


x- / 


\ ^ / 










A 


\/X 


''///S 

/ 11/ 










y\ \ 










\/, 




r "^v 




v^ 








,0 * /\ 






\y/ 






% / 










\ ^ 




/\ \ 

C s / 

\ \ / 








\/ 


/x 


















\ / 


'X /N 




\ / 




\ / 


N / 










\ / 



0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 

(c) |x' 



s'max 



100.0 



50.0 



20.0 



10.0 



5.0 



2.0 



1.0 



0.5 



0.2 



0.1 



\ / 






y\ 












4 / 




\ / 


\ 








j&/ 










/x 






/ 








,vv 






/^S? 






\/ ' p 


\ / 


\ / 












^i<Sx 






















, <ix g i 














N v / 




si? 




ss% 


> /\< 






\ / 




\ / 


\ / 




'Ik 










/ »4 % 


o 










s X. / 




"% 


















\ / 


/\& 


s ? 








\ / 


o 




y\%- 







0.01 0.02 0.05 0.10 0.20 



0.50 1.00 2.00 
Frequency, CPS 

(d) <|xj> 



5.00 10.00 20.00 511.00 LOO. 00 



Fig. 2.27 (Continued) 



100.0 



50.0 



20.0 



10.0 



¥ 5.0 



1 2.0 



1.0 



0.5 



0.2 



0.1 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 

(a) |x„' 



s'max 



100.0 



50.0 



20.0 



10.0 



5.0 



J* 2.0 



1.0 



0.5 



0.2 



0.1 



\/ 






v\ 












4 / 


< > 





A 








\^x 














A 










#V 






Y^< 






/x" 5 




































TUlrZ 




/x 












\ / 






Y ' / 


</*% 


\ s 








\ / 




\ / 


N v' 






\o c / 




<l*fll 

N / 


>/\ 










6 


V 


x\ ll 4 


' x^\ 


"Xb 






















s / 






\ / 


\ / 




\ / 


\ / 




\ / 



0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 

(b) <|x s |> 

Fig. 2.28 Elastic Hydrodynamic Parameter Response Spectra. 
Taft Earthquake. 3 , = 0, 1, 2, 5, 10% 



182 



100.0 



50.0 



20.0 



10.0 



c 5.0 



•* 2.0 



1.0 



0.5 



0.2 



0.1 



\/ 
















^ / 






A 


NA-v* 






















ye, /\ 


\ / 




^V- 










S / 


XV. A. 

Ax*- X 












t- -k$ 




v 7 


s^O 


**- 








\ "^ 








if r^ 




[ g max 
/ \ 




\\X V 

^\A^\/ 








\ / 




1 / 4 


$■' 


v% 


\ / 




xy\ 


p 


■^ / 






\ / 


A ^\ 




4> ? 










\ ^ 


A^\ 


N> ' 


\. 


A 


/\ / 








\/ 










'xx/ 




\ / 










\ / 


\ / 






\ / 







0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 



100.0 



50.0 



20.0 



10.0 



5.0 



2.0 



1.0 



0.5 



0.2 



0.1 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 

(H) <|x s |> 



Fig. 2.28 (Continued) 



looo.a 



500.0 



200.0 



100.0 



50.0 



E 20.0 



10.0 



5.0 



2.0 



1.0 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 



s'max 



100.0 



50.0 



20.0 



10.0 



!rf 5.0 



— 2.0 



1.0 



0.5 



0.2 



0.1 



s / 






v\ 












% / 










?" \ 




*$/ / 










%? 


1 V 




s / 


\ 


S / 


s / 


^^ 






>r^ 




\ / 


x/ ' & - 


s. 

\ / 


























v 










-7 ^\ 
ij S 


/x 




^<"' 








A 








^/\& 




g 1 
IS / 












N v' 




{/ s 


\o c / 




















x / X 


/ \ 


y<o 












' \ 






N / 


X 1 ^ 


' \ 






\ / 






s / 









0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 

(b) <|x s |> 

Fig. 2.29 Elastic Hydrodynamic Parameter Response Spectra. 
Ferndale Earthquake. $ total = 0, 1, 2, 5, 10% 



184 



100.0 
50.0 

20.0 

10.0 
at 

c 5.0 

X 

<o 

_E 

l/> 

•JL 2-0 

1.0 
0.5 

0.2 



0.1 







\$ 














« x 






v 


X ^ 

L v^ 


* X 
















av 




/^X, 






yS^ - . 












X •? 










s / 




IS X 








' »*> 




\ . y 


£> X> 

VqA 














>X / i 




■J-Jt 








n\x X 

^ N \ y X 

y ^ N X A 
% < \X 










• \X" 






x^3 






$X \/ 


\\ 








Xx 






(p / 
\<%>/ 










x^Cv 












%> 
















v' 


\ X 




\ X 


\ / 






\ / 




\ x 






s / 



0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 

< c > XLax 



100.0 



50.0 



20.0 



10.0 



5.0 



2.0 



1.0 



0.5 



0.2 



0.1 



N A 




N A 


XX 








\ X 




4 x 








X \*\ 

A X 1 


*■' x. 




\^X) 










/% 






\/ 


r t&\ 






Sfx^ 






^XX^ 






x ' & 




A 

\ / 










X>S?1 














A 












/Ast> / 




AX^ 














fff\ 


X <l ^ 1 


> \> 


\\ X 


~V/X 

§x \/ 










\ X 




X ^\ 

v X 


'trv' 








\ / 


\ ^ 










/ <t l 

X / 


A 


y(o 








A \ 


\^X 








S / 




X 


S X 




s } 










<$x 





0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 

W <|x s |> 



Fig. 2.29 (Continued) 



1000. cv 



500.0 



200.0 



100.0 



50.0 



u, 20.0 



10.0 



5.0 



2.0 



1.0 




0.01 0.02 0.05 0.10 0.20- 0.S0 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 

(a) |x c l 



1000. 



500.0 



200.0 



100.0 



50.0 



20.0 



10.0 



5.0 



2.0 



1.0 



C X, I 






v\ 












4o? 


/\ 


6 
















X / 














^ \ 




^&S 
























/\ 












- 1 /\ 


\ / 












\ / 


^x 


\ / 


\ / 




\ / 
















vX X/ 1 










\/ 








xyx y 














X 








/^ X 






















C— > 


\-7> 


u <~x g l>" 


C--^ 


X-*,.r ' 


^w— , / 












'ef 




































§/ X/ 




\ / 




\ / 












\ / 









0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 
(b) <|x s l> 

Fig. 2.30 Elastic Hydrodynamic Parameter Response Spectra. 

San Fernando Earthquake. 3 total = 0, 1, 2, 5, 10% 



looo. a 



soo.o 



200.0 



100.0 



50.0 



20.0 



10.0 



5.0 



2.0 



1.0 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 

M l*.L.„ 



1000.0; 



500.0 



200. 



100.0 



5! 50.0 



20.0 



10.0 



5.0 



2.0 



1.0 




0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 5.00 10.00 20.00 50.00 100.00 

Frequency, CPS 

(d) <|X.I> 



Fig. 2.30 (Continued) 



187 




to 

Q. 

o 



>> 
o 

c 

3 

cr 

<v 

S- 



+-> 

CD 

E 
<u 
o 
to 

a. 
«/> 

•r— 
Q 

<o 

S- 

o 



a 

CD 

Q. 

co 

a> 
to 
c 
o 
a. 
to 

O) 

a: 

s- 
a> 
+-> 
a; 

E 
rO 

S_ 
(O 



E 

<TJ 
C 
>> 

T3 
O 

S- 

■o 



T3 
CD 
N 



CD 

■a 



«4- 
O 



+■> S_ 
O CD 
=J 4-> 
S- CD 

■•-> E 
to <o 
c s- 
o <o 

o a. 



CO 
CNJ 

CD 



(<| S x|>co J0 XBU, | S x| m ) 
£}L30|9A 



188 




Q. 

o 



>> 

o 

c 
<d 

3 
O" 
<D 

s- 



CD 



10 

CD 

q: 

CD 
4-> 

CD 

E 
ro 

S- 

m 



E 
rO 

c 

>> s- 
-o <u 

o ■«-> 
S_ CD 
-O E 
>> 03 

n: s- 

"O Q_ 

CD 

N >> 
•i- +J 

rO o 
<D O 
TJ i— 
i— i CU 

O fO 

C i. 

o o 

•i- 4- 
O E 

X- S_ 
4-> +-> 
(A O 
E CD 
O Q- 
O O0 



CM 
CO 



CM 



o> 



«| s x|> ao ^| S x|) 



189 




c/> 

£= 
O 
•r— 
4-> 
(O 

'a> 

c 
o 

•r— 

E 

o 

n- 

0) 
Q 

I 

CD 
O 

c 
<c 

■M 
to 

•r— 
10 

CD 



to 



o 

4-> 
CO 



CO 

cvj 



•r- 



aouB^s|.say 



i 



190 




o 
o 

d 
o 



o 
o 



o 

LO 



o 
o 



o 

CM 



o 
o 



o 
o 



m 



o 



d 



CD 
«d 

cr 

i- 



o 

c 



LU 



o 




<o 


r-> 




S- 






-l-> 


CM 


CO 


o 




Q_ 


01 




O 


a. 

CO 


n 


• 




o 


>- 


o> 


• 


o 


CO 


w-l 


z 


c 


o 
in 


3D 

o 

UJ 

u. 


o 

Q. 

to 

a> 

OS 


d 




stic) 
0.00 


o 




<T3 II 


CM 




Q_ ^ 


o 




sto- 
max 


O 




<o 


~-* 




i— CD 


* 




uj :x 


o 






o 




'£ CM 


o 




rtJ 
r— II 

0> 

C CO 

i— i oa 


CM 

o 




«3- 



CO 

CM 



o> 



O 
O 



a 

in 



D 
CM 



O 

d 



a 
in 



o 

CM 



in 
d 



CM 



o 



03S/NI 'UI3CTGA 



191 




o 






o 






o 






"■* 






o 






o 




9\ 


o 

LO 




01 
J* 


O 




+-> 


O 




S- 






<o 


O 




UJ 


C\J 




o 


O 




+J 


o 




c 


• 




01 


o 




o 






LU 


o 






o 




(O 


LD 




-p 
u 

01 

Q. 
CO 


O 






O 




01 
M 


(M 


en 


C 




Q_ 


o 




O 


Q. 
t/> 


O 


» 


Ol 


O 


>- 


q: 


• 


o 


10 


-^ 


~z 


--oO 




UJ 


o o 


o 

LO 


o 

UJ 

u. 


asti 
= 0. 


O 




Q. S£ 
O X 
to E 


n 




UJ 


01 




i— en 






uj :x 


o 




Q 








* 




rtj 


o 




1— II 
01 

1— 1 CO. 


u> 






o 






o 




LO 

CO 

• 

CM 

• 


CVJ 




C7> 


o 




■r"" 



o 

o 



. 


o 


o 


o 






o 


« 




• 


o 


o 


o 


o 


d 


o 






•— * 


LD 


c\j 


*— • 


LP 


(\J 



LO 

d 



r\j 

* 



D3S/NI 'JL1I3013A 



192 



x\ 


yv 








/^ 


'\ S X 




\/ 






^\ 










X\ A 


A 

kx 7 
<?x 


\$? 


& y 








/ \ 




















x < 


X \ 


\ / 




>v / >^' 


X X 


XX^ 


X\ /^ 










>Q 


a/ 


LO \ N 

7/ " J 


// > /<■ 


^X / 
















/Nl \ ' 


^ »e ^\ 










C 


\/ 


<j\ y\ 




l\ -/ N. ( 


L<X\ 

7 \ 








d^/ 










\\ • 




s^X J) 






V\ \v 










Xs' 




o 
















\S N 










\/ 




\/ 






\/ 



o 
o 

d 
o 



o 
o 



o 
in 



o 
o 



o 



o 
o 



C\J 

o 



O) 






O 

S- 
+J 

c 

<D 

<_> 



o 
o 






LO 




o 

<U 
Q. 


O 




(/) 


o 




c 
o 


C\l 


en 


OL 




Q_ 


</) 




O 


<u 


n 


• 




o 


>- 


CO 


• 


o 

2 


o o 








LtJ 
Z3 


+J o 




O 


C/> 


o 


UJ 


nj II 


ld 


(XL 

U- 


Q_ iZ 


o 




O X 

4-> «J 
t/> E 

i— OT 


o 




uj :x 


Ol 




» — Q 






i£ 


o 




stic 
02, 


o 




fO 


— -• 




1— II 


• 




<u 


<_> 




i— i oa 


LO 
O 




iO 

CO 



CVJ 



O* 



o 
o 



o 



D 



O 

d 



o 



o 



in 
d 



r\j 

« 



D3S/NI 'X1J3013A 



193 



TV 










/N 




















\ x / 










^\ 






\ / 




/\ A 


<?x 






/ \ 


\/ 




V N 








\f* 
































^\ > 


\ / 




\. / \« 


vXVm 






















/\ A- 


<?x 
















&/ \ 








/ \ 








/\\ \* 


»v/ \. 








\ / 




X\ $ 


*^\ <" \ 


X *\ /\ 

K ^X " \/ ^ 














'^.-"SA^ VTI 












G*y/ 




/Si 

* 






/ \ 


>\ 4 

\$>x 






0\ 




/ ^ 












-/ ®< 


j( \. 










\s/ 




vy 
















\ / \< 


<#*\ 
r 














\/ 




\/ 



o 
o 

d 
o 



o 
o 

d 

ID 



O 
O 



O 
OJ 



o 

o 



OJ 

o 
d 



o 
o 






o 

s- 

c 



o 
o 




to 

i. 
+-> 


LD 




u 
ai 
a. 

CO 


O 




<o 


O 




c 
o 


CM 


CO 


Q. 




Q_ 


CO 




o 


a: 


o 


» 




o 


>- 


—nO 


• 


o 

-z. 

o 

UJ 


a lo 


o 


asti 

= 0. 


in 


LX 


o. ^ 


o 




lasto- 
g max 


o 




lxj :x 


OJ 




Q 






i£ 


o 




stic 
02, 


o 




fO 


n 1 




1— II 


• 




<u 


o 




c to 

i—i GO. 


O 




co 



CNJ 



D> 



O 
O 



O 
LO 



D 
OJ 



O 

d 



o 



o 

* 
OJ 



o 



OJ 

d 



D3S/NI *JU.I30T3A 



194 




o 
o 

d 
o 



o 

o 



o 

LO 



o 
o 



o 

OJ 



o 
o 



- o 



o 
o 



LO 



LO 

o 



OJ 
O 



o 
o 



Lf> 



II 

3- 



o 



CO 

QQ. 



3 
O" 

-C 
■»-> 

s_ 

LU 

o 

&- 

4-> 

C 
CD 

o 



LU 



o 




•s 


f 




<o 


OJ 


CO 


S_ 




CJ 


o 


o 
o 


>- 

o 


Q. 

co 


( 


2 






LU 


<u 




ZD 


CO 




o 


c 


o 


LU 


o 


in 


cc 


o. 




u. 


CO 


d 




o 


o 




4-> 


OJ 




to 


• 




(O 


o 




1 


o 




o 


""* 




CO 


n 




fO 



o 

CO 
fO 



00 
CO 



CVJ 



C7> 



O 

o 



o 

LO 



D 



O 

o 



o 

LO 



o 



O 



LO 

d 



« 



03S/NI 'JL1I30H3A 



195 




o 
o 

d 
o 



o 
o 



o 
in 



o 

CM 



o 
d 



o 

IT) 



o 

CM 



in 



o 




o 








o 




CVI 


LO 




II 

ft 


O 
O 




CM 
O 


O 




• 


CM 




II 

CO 


O 




CO. 


O 






• 




f| 


o 




cu 






3 


o 
o 




JZ 
+-> 


LD 




S- 

<a 

LU 

o 


O 




4-> 


n 




C 






CU 


CM 


en 
a. 


o 




o 


UJ 


o 


» 




r> 


>- 






o 

UJ 

3 


4-> 




C3 


O 


o 


UJ 


CD 


in 


rx 


CO- 




U- 


GO 


d 




(/> 

c 
o 
a. 


o 




</> 


CM 




0) 


« 




en 


o 




o 


o 




4-> 


«— 1 




00 


o 




ro 
Q_ 


in 




O 

4-> 


d 




l/> 
<T3 



CM 
O 






CM 

* 



D3S/NI 'UJOCTQA 



+-> 

c/> 
fO 

'a; 



ro 



CM 



o> 



196 



/\ 










/^ 


< 


\y\ 

U3 


/ 


^ 

/ 






i^\ 








C C_J UJ C_3 
/ O O O Lf) 

./ OOO O s 
\ II II II II 


\¥ 


4/ \ 




k^ 






JT A ^ ^ ^i i^ 

\/ XXX X 

.X fO <U fO (O 

\ E E E E, 












\ / 




< :x :x :x 

Q Q O O 
<. -^ iZ ^ 

/ 


/\ 


^\ / >v* 


y \ 


A , 












s 


X* 






/\N 


^/ / 


/ \ 


< 






\ / 


/x ' 


Ta\ / 






\ / 










V^ / \< 


^x \ 








o~\/ 




/ \ 
















•S/ N. 










y^ 




\. / 
















\ / \ 










\/ 




\/ 


\/ 




\/ 

















n 













*-* 




















<a- 


lo 




11 







CM 







O 


* 













C\J 




II 

00 







GO. 









• 




0% 







CD 






3 










LP 




s- 

LU 
O 

s- 


O 




+J 


O 




c 

CD 


CJ 


CD 

Q_ 


O 




O 


UJ 


O 


* 




n 


>- 


ft 


»— * 


CJ 

2 







ZD 
O 
UJ 

tr 


O 

CD 




u. 


CO 


O 




CD 
V) 

c 


Q. 


O 




CO 


r\i 




CD 






C£ 







O 


O 




•»-> 


v~l 




CO 


« 




IO 







a. 


LO 

O 






CO 



C\J 

o 



o 
o 



o 
o 



o 



o 

(\J 



o 
d 



o 

Lfl 



o 



in 
d 



t\j 
o 



03S/NI 'JL1I3013A 



CO 

CD 



O 



CNJ 



O) 



197 





•4 

1 " 

— « 


1 

1 

1 
1 


equency 

ge 

1 1 




• 4 


1 

1 
i 






High Fr 

Ran 

1 1 1 


I 


i— LO 

o o 
o o 
II II 

CO CO 

00. CQ 

• ♦ 








1 

1 

1 








• 4 


1 




equency 

ge 

1 1 


1 








1 " 
1 '* 




Mid Fr 
Ran 

i i 1 












4) 
4» 


h i 


equency 

ge 






W 1 ... 


Low Fr 
Ran 

i I 1 



o 






in 






in 






^r 


o 




■51- 




"O 


i 


CO 


E 


CO 


03 


rc 


CO 


S 


S^ • 


C\J 




+J O 

•r- <d- 
O CD 


CM 
1 




O r— 






d by Ground Ve 
ro Earthquake, 


1 




CU 4-> 
N E 


LO 




•i- CU 


LO 




03 
CU i— 


«d- 


o 


E LU 




z 


_J 


<d- 




— -> . 


1 


10 


_J 


ro 


CO 


E i— 




03 


O 


CO 


S 


■r- E 
+J CU 


CM 




3 +-> 
i— CO 

<2 >> 


C\J 




co CO 






of Linear Drag 
rag Solution, 
nt. 


i 




Q CU 
E E 


in 




O S- O 
CO 03 Q. 


in 




•r- CU E 
S- E O 


<d- 


• 


03 «r- C_) 


o 


CLi— 




zr 


E e co 


<3- 




O O 1 


i 


CO 


o z z: 


co 


CO 

03 




CO 


s: 


,_ 


CM 




CO 


CM 
1 




CD 



o 

CM 



O 
O 



o 

CD 



O 
00 



(6eurj J69ULLU0N) uolijoislo 6uuds 'xen 
(6e»ia JC9un) uo!4joislq 6uuds *xew 



198 





T 
| 

i 


» 


requency 
nge 




< 
< 


► 1 






High F 
Ra 

1 I 1 




i— in 
o o 

o o 

ii ii 

to 10 

CQ. CO. 

• ♦ 






I 










i 
I 
1 . < 






r 

■equency 

ge 

1 1 










i 
l 

• < 




Mid Fr 
Ran 

i i 1 














A 1 


requency 
nge 

1 1 






V 1 
• ♦ 

• ♦ 1 


Low F 
Ra 

, . 1 



ej 






LT> 




+-> 


LO 




1 c 


«-j- 


n 


O E 




o 


^ o 




z 


Q. 


«a- 




■a e 


i 


to 


c o 


ro 


to 

03 


03 O 


CO 


^ 


---*co 

>> 1 


CvJ 




a *> 


CsJ 

1 




o o 

1— «3- 






d by Ground Ve 
Earthquake, 19 


C3 




CD 
N O 


LO 




•r- S_ 
s- +-> 


LO 




03 C 
CD <U 


*d" 


o 






■z. 


_l i— 


1 


CO 


UJ 


CO 


CO 


ez 




OS 


o • 


CO 


s 


•i- s: 

-M i— 


CvJ 




3 

<— E 
O CD 


CVJ 

1 




00 4-> 
CO 






of Linear Drag 
Solution. Sy 


CJ3 




en 

E 03 


LO 




o s- 

co Q 


lo 




Z. S- 


<d- 


o 


03 03 
Q. CD 




z: 


E c 


«3- 




O i- 


1 


LO 


O i— 


CO 


CO 

03 




CO 


s 


CNJ 


CO 
C\J 

1 




CO 

en 



o 

CO 



o 
o 



o 

CM 



O 
00 



(6ejQ jeauL[U0N) uol:mo:islq 6uuds # xew 
(6ejQ ueaun) uolijoislq Buuds 'xew 



199 





i « 


► 


: requency 
mge 

1 1 




i 


v 

► 






High F 
Re 

1 .1 1 




i— LO 

o o 
o o 
II II 

CO CO 

QQ CQ 

• ♦ 
















• 4 
• 4 






"equency 
ige 

1 1 


■ 








1 •* 

• i 


1 


Mid Fi 
Rat 

1 1 1 












< 


» 

k * I 


c — 
co 

cr a> 






1 

* ♦ 1 
► ♦ 1 


s- c 

o — 

_J 



o 






LO 




4-> 


LO 




1 c 
c cu 


«3- 


• 


c: 




o 


z 




zz. 


Q_ 


<tf- 




■0 E 


1 


CO 


c 


CO 


CO 


ro C_j 


CO 


s: 


--^lO 
>> 1 


CVJ 






C\J 




O O 

1— «d- 






d by Ground Ve 
Earthquake, 19 


1 




CU 
N O 


LO 




•1- S_ 
S- 4-> 


LO 




rO C 
O) CD 


«^- 




C O 










o 


_! , — 


<d" 


z 


LU 


CO 


CO 


C 




CO 


O • 


CO 


fO 


•r- _l 


s: 


+-> CM 


CVJ 




3 

«— E 

ai 


CVJ 

1 




CO 4-> 
CO 






of Linear Drag 
Solution. Sy 


cu 
1 




en 
c ro 


LO 




s- 
co Q 

•r- 


LO 




ro ro 


«3- 


. 


Q. CD 




o 


E c 


«tf- 


2: 


O 1- 
O 1— 


co 


CO 
CO 

rO 




ro 


S. 


CO 


C\J 




ro 


CVJ 

i 




en 



o 

CVJ 



o 
o 



o 
cr> 



o 
00 



(6t2JQ JB9UL[U0N) UOL^JO^SLQ 6ULJdS 'XEW 

(BejQ jeaun) uol^uo^slq Buuds *xbw 



200 





1 

< 

| « 




•equency 
ige 




« 


r-' ■ " . 

> 






High Fr 
Rar 

i i 1 




i— Lf) 

o o 
o o 
II II 

to t/ 

CQ CQ 

• ♦ 
















• ♦ 
• 4 






s 

E — 
CD 

cr (D 










1 ** 
• 4 


P - -■ - — 

1 


S- E 
U_ fO 












•0 
•0 


A • 1 


'equency 
ige 






• ♦ | 

• ♦ 1 

1 


Low F» 
Rar 

i I 1 



C3 






tn 




+-> 


lo 




1 E 

E CD 


^i- 


o 


O E 
Z O 




z 


Q. 


«sr 




T3 E 


i 


to 


E O 


CO 


to 


fO O 


CO 


2a. 


'-^OO 
>> 1 


CvJ 






CVJ 

1 




o o 

1— *3- 






d by Ground Ve 
Earthquake, 19 


as 
i 




CD 
N O 


LO 




•r- S- 


Lf) 




tO E 

CD CD 


«*1- 




E <_> 










o 


_l r— 


«* 


z 


LU 


CO 


to 


E 




to 


O • 


CO 


rO 


•r- ^ 


ze. 


-t-> CVJ 


CVJ 




3 

>— E 
O CD 


CM 
1 




00 +-> 
CO 






of Linear Drag 
Solution. Sy 


C3 
1 




en 

E (0 


Lf) 




o s_ 

V) Q 


Lf) 






"3- 


• 


rtj fO 


o 


Q- CD 




z 


E E 


*d- 




O i- 


i 


to 


O i— 


CO 


to 

fl3 




CO 


zz. 


«3- 


CVJ 




co 


CVJ 

1 




en 



o 

CvJ 



O 
O 



o 



o 

CO 



(6euq ueauL[U0N) uol^jo^slq 6uuds 'xew 
(6buq jeaun) uol^uo^slq 6u.L*ids *xew 



201 





T 

1 • « 

1* < 


1 
1 
1 
1 


requency 
nge 




• 4 


1 

1 

i 






High F 
Ra 

1 I 1 


| 


i— Lf> 
O O 

o o 
II II 

10 to 

00. QO 

• ♦ 






1 


1 

I 

1 








1 . < 
1 

1 ' * 
_L _ 


1 




equency 

ge 


1 

1 
1 








- - 1 < 

1 
1 

• 4 


w 

► I 


Mid Fr 
Ran 

l l 1 












A 


• 
« 1 

A A 1 


equency 

ge 






1 

•♦ 1 
•♦ 1 


Low Fr 

Ran 

i I 



C3 






IT) 




• 


LO 




i e 

c cu 


«^- 


• 


O E 




O 


Z O 




Z 


Q. 


*a- 




-a E 


i 


to 


E O 


ro 


to 
re 


03 <_> 


ro 


s: 


--^GO 

>> 1 


CM 




•r- 


CM 




o o 






by Ground Ve 
arthquake, 19 


o 




0) 


IT) 




N O 
•<- S- 
S- 4-> 


I 




03 C 
<D CU 


«* 




C O 




• 


•r~ 


<* 


o 


_l i— 


z 


UJ 


ro 


to 


c 




to 


o • 


CO 


os 


■I- _J 


s: 


+-> CO 


C\J 




3 

>— E 
O CD 


CM 

1 




OO 4-> 
V) 






of Linear Drag 
Solution. Sy 


1 




CD 
C 03 


m 




to S 


IT) 






^J- 


• 


03 03 




o 


Q. CU 




z 


E c 


«tf- 




O t- 


1 


to 


C_) i— 


ro 


ro 




CO 

i 


s: 


Lf> 


CM 




CO 


CM 
1 




CD 



o 

CM 



O 
O 



O 
CD 



O 
00 



(6eaq UBgULjjJOjj uol^uo^slq 6uuds 'xg^ 
(6ejQ ueaun) uol^uo^slq 6uuds *xew 



202 





1 

l» ♦ 

1 * 4 

m 4 




'equency 
ige 

1 1 




i * 

• 4 








High Fr 
Rar 

i i 1 




i— LO 

o o 
o o 
II II 
co co 

OQ. QQ. 

• ♦ 






1 










• 4 

1 

1 • ♦ 






jquency 
je 

1 1 


. 








1 • • 
•4 

• ♦ 


1 


Mid Fn 
Rant 

i i l 












« 


♦ • 
• * l 


"equency 
ige 






♦ • | 

1 
•♦ 1 

| 


Low Fi 
Rar 

i i 



C3 






LO 




+-> 


LO 




1 c 


*3- 


o 


o c 
z o 




•ZL 


Q. 


*3" 




T3 E 


1 


CO 


C O 


CO 


CO 


(O C_> 


co 


:*. 


--^oo 

>> 1 


CM 




+-> 2: 


CM 

1 




o o 






d by Ground Ve 
Earthquake, 19 


o 




CO 
N O 


LO 




■r- i. 
S- -M 


LO 




CD CI) 


*3" 


o 


SZ O 




z 


_J l— 


i 


CO 


LU 


CO 


CO 


c 




TCI 


o • 


co 


s: 


•r- _J 




-»-> «3" 


CM 




3 

■— E 
O CO 


CM 
1 




GO +-> 
CO 






of Linear Drag 
Solution. Sy 


CJ3 




en 


LO 




o s- 

co Q 


LO 






^J- 


o 


a. cu 




z: 


E c 


«3" 




O i- 


| 


CO 


O 1— 


CO 


CO 

03 




CO 


s 




CvJ 




CO 

• 

CO 


CVJ 

1 




. 



en 



O 

CM 



o 

O 



O 

cn 



o 

oo 



(6euq jb9ul[uom) uolijoislq 6uuds 'xe^ 
(6bjq ueaun) uo.l^Jo^slq buwds *xew 



203 





1 
•1 

1 


♦ 










— 




1 • 

1 


4 

4 








equen 
ge 






1 


^ 








s_ c 


— — 












U_ (T3 
















cc 






I 










-C 






<• 

I 


♦ 








CD 
•i — 

DC 


~~ " 






4 












— 


i— LO 






I 
























O O 










i 








• • 










i 








o o 










i 








II II 


















tO V) 










I 








on oq. 


















• ♦ 










I . 


♦ 




























>> 
















o 
















c 








• « 








CD 

cr cu 

<L> CD 


— 






A A 








S- E 








W '^ 








U_ 03 
















C£ 
















"O 
















•r— 








1 


► 






s: 


— 




• 


♦ 
















< 


♦ 


♦ • 


A 


>> 

o 

c 
(I) 

cr a> 


— 










r 


^ 


-■ ■ CD CD 














s- c 
















Ll_ n3 
















0£ 












♦ | • 


o 


— 










1 




_l 












•♦1 
1 






- 



cu 






LO 




-M 


LO 




1 C 


«a- 


O 


o c: 
z o 




Z 


Q. 


"3- 




-a E 


1 


10 


c o 


CO 


to 

03 


03 O 


CO 


s: 


>> 1 


C\J 




o « 


C\J 

1 




o o 

1— sj- 


1— 




d by Ground Ve 
Earthquake, 19 


cu 




CD 
N O 


LO 




■r- S- 


LO 




03 E 
O) CL) 


*d- 


o 


•r— 




z 


_J i— 


**• 
1 


to 


UJ 


CO 


to 


c 




03 


o • 


CO 


S 


■i- s: 




+j «a- 


CM 




i— E 
O CD 


CM 
1 




CO +J 

to 






of Linear Drag 
Solution. Sy 


CU 




CD 
C 03 


LO 




O S_ 
to Q 


LO 






"vf 


. 


03 03 
Q. CD 




o 


E c 


1 


SI 


O t- 
O I— 


co 






CO 
1 


03 


r-». 


CM 




• 

CO 


CM 
1 




CD 



o 

CM 



O 
O 



O 
CM 



O 

CO 



(6gJQ Ue9UL[U0N) U014J01SLQ 6ULJd$ *XBM 

(6euQ ub8ul-|) uol^Jo^slq buuds *xew 



204 





• ♦ 

• 1 ♦ 




1 
1 
1 
1 


'equency 
ige 




1 

• 4 




1 

1 

1 


1 

High Fr 
Rar 

i 1 




• 4 




1 
1 






— 


1 


0.01 
0.05 










1 
1 












1 


II II 












1 


CO tO 

oa co. 












1 


• ♦ 








• ♦ 




1 







1 








1 • 

- 4 


* 


1 
1 
1 


>> 

c 

OJ — 

cr <u 
Q) en 




1 • " 




1 

1 
1 


Mid Fi 
Rar 




• ♦ 




1 
1 

1 

I 







< 


» 


1 
1 

1 

1 
1 

1 

1 


"equency 
ige 

1 1 








1 

1 
1 ♦ • 

1 


U_ 03 

2 
O 

_l — 








1 

1 •♦ 

1 


- 



o 






in 




-M 


LO 




1 c 

C CD 


«3- 


• 


o c 




o 


21 O 




21 


Q. 


<d- 




■O E 


i 


LO 


c o 


ro 


to 

<T3 


«3 CJ 


CO 


s: 


<-~>co 

>> 1 


C\J 




-i-> 2: 


C\J 

i 




o o 

r— <3" 






d by Ground Ve 
Earthquake, 19 


cu 
1 




N O 


LO 




•i- S_ 


LO 




«3 C 


<3- 


o 






21 


_l ■ — 


*d- 
1 


to 


LU 


CO 


to 


c 




<o 


o • 


CO 


^ 


•r- nr 




+-> «3- 


C\J 




13 

r- E 
O 0) 


C\J 

1 




CO 4-> 

to 


I— 




of Linear Drag 
Solution. Sy 


CD 




en 


LO 




o V- 
to Q 


LO 




£ s- 


«=d- 


• 


n3 (O 


o 


Q. CD 




21 


E c 


<5j- 




O -r- 


1 


• 


O r— 


CO 


to 
to 




CO 




CO 


C\J 




CO 


1 




en 



o 

CVJ 



o 
o 



o 

CD. 



O 

CO 



(6e>i.Q jp9ul[uon) uoL^uo^sLg 6uLJd$ -xe^ 
(6ejQ uegun) uol^Jo^slq 6uuds *xew 



205 





• 




♦ 


1 
1 
1 
1 







• 




♦ 


■equency 

ge 

1 






• 


♦ 


1 

1 

1 


High Fr 
Rar 

i 1 






• 


♦ 


1 
| 






— 










1 
1 


0.01 
0.05 














1 


ii ii 














1 


QQ. QQ. 














1 


• ♦ 














1 




— 


* 1 












• ♦ 


1 

| 


>> 
u 

c 

CO ~~ 








a 4 


1 


3 

a- a> 








• ♦ 


1 

1 
1 


Mid Fr 
Rar 

1 1 








• ♦ 


1 
1 

1 

1 










« 


1 

1 

_ 1 

! 

1 ♦ • 

1 

i j 


f 
• 

Low Frequency 
Range 










l < 
1 

1 ♦ 
i 










i •♦ 
j 





CD 






LO 




4-> 


lo 




1 a 
C CO 


*f 


• 


o c 


o 


^ o 




■21 


Ol 


•=j- 




-O E 


i 


00 


c o 


co 


00 


<TJ O 


CO 


s: 


>> 1 


CM 




•r- 


C\J 

i 




o o 

1— «3- 






d by Ground Ve 
Earthquake, 19 


1 




co 

N O 


LO 




•r- S- 


LO 




CO (1) 


^t 


• 


c o 




o 


■t^ 




z: 


_i i— 


1 


to 


LU 


CO 


co 


c 




<o 


o • 


CO 


s 


•r» re 




+J LO 


CM 




3 

>— E 
O CO 


C\J 

1 




CO 4-> 
CO 






of Linear Drag 
Solution. Sy 


o 




en 


lo 




O S- 
to Q 


LO 




•i — 
S- s_ 


«3" 


. 


fO <o 


o 


Q. CO 




^ 


E c 


*3- 




O -i- 


1 


CO 


O i— 


CO 


CO 




CO 
1 


s: 


en 


CM 




co 



CM 



CD 



O 
CM 



O 
O 



O 



o 

00 



(6ejq ue9UL L uoN) uoL^uo^SLg 6uuds 'xew 
(6pjq aceun) uo.14J01s.LQ 6uuds *xew 



206 





1 
!• 

1 


♦ 


1 

1 
1 




>> 
O 

c 


— 




1 
1 


4 


1 
1 




reque 
nge 






•i 


^ 


, 




l_l_ <u 












OC 










1 




JZ 






J 
i 


♦ 


1 




en 

in 


— 




i 


• 4 


1 

| 








— 


r— in 






| 


















1 


o o 










i 






• • 










1 






o o 










1 




1 


II II 














I 


10 io 










| 




1 


CQ CO. 














1 


• ♦ 










i 

■ 


• 4 


1 
1 






— 








1 




1 




>> 






1 

1 


—• «■ 


1 
1 




o 

c 

CD 

3 

cr CU 






i 


^w 


1 




Li_ rd 








• ♦ 


1 
1 




-o 

•r— 


— 






• ♦ 


1 

r 

i 














i 
i 
1 — 

••I 














♦ • i 
i 




>> 

o 

c 

0) 

3 

cr Q) 


- 








M 
















s_ c 










i 




Ll- 03 










1 




Q£ 










* 1 
1 




2 

o 

_l 


— 








♦ 1 

I 


• 




- 



o 






in 




4-> 


in 




1 C 

c cu 


«3- 


• 


o cr 




o 


2: 




z 


Q. 


«3- 




T3 E 


i 


10 


C O 


co 


10 
03 


03 C_> 


co 


s: 


— *CO 
>> 1 


CM 




u « 


C\J 

1 






r— «xt" 






d by Ground Ve 
Earthquake, 19 


CD 

1 




M 


m 




•r- s- 

S_ -t-> 


in 




03 C 
CD CD 


«d- 


o 


E CJ 




SI 


_1 1— 


i 


(A 


LU 


CO 


10 


C 




03 


O • 


ro 


2L 


•r- s: 




4-> IO 


C\J 




3 

1— E 

ai 


CM 

1 




00 +-> 
10 






of Linear Drag 
Solution. Sy 


CD 




en 
c fO 


in 




O S- 
10 


in 




•r— 


«3- 


• 


03 03 




O 


Q_ d) 




z: 


E c 


*d- 




O T- 


i 


1/5 


O 1— 


oo 


03 




CO 

1 


S 


O 


CM 




• 

CO 


CM 
1 




en 



o 

CM 



O 
O 



o 

CT> 



O 

CO 



(6bjq jb9ul[uon) uol^jo^slq 6uuds *xbw 
(6buq jieauL"]) uol^Jo^slq Buuds *xbw 



207 





1 

• 


♦ 


1 

1 
i 


>> 
O 


— 




• 


♦ 


1 
1 


c 
cd 
3 
cr cd 


— 






A 


l 


CD CD 








w 


1 


Ll_ fO 










1 


cc 












-E 






• 


♦ 


1 

1 


CD 


— 






• ♦ 


1 
1 








— 


| 


i — LO 










1 
















O O 
















• • 














1 


o o 














1 


II II 














| 


to to 
















QQ. QQ. 














1 


• ♦ 












• 4 


1 




-I 


— 


1 












1 


>> 








• 


1 


o 
c 
cu 

3 

cr cu 


— 






m * 




Qj CD 








• ▼ 




S- e 








• ♦ 




-a 

2: 


— 






• ♦ 














♦ • 


>» 

CJ 

E 
CD 


- 








♦ 1 • 


Frequ 
ange 










1 A A 


(Y 










• ▼ 


O 

_l 










1 <" 




— 








1 ♦ 
| 


• 


- 



o 






LO 




+-> 


LO 




1 E 

E CD 


«^- 


o 


O E 
Z O 




z: 


Q. 


*3" 




-a E 


1 


to 


E O 


CO 


to 


fO O 


CO 


s: 


-— ^oo 

>> 1 


C\J 






C\J 

1 




o o 
r— *a- 






d by Ground Ve 
Earthquake, 19 


o 
1 




CD 
N O 


LT) 




•r- S- 
S- 4-> 


LO 




re e 

CD CD 


<d" 


d 


E O 




z 


_l f— 


1 


to 


LU 


CO 


to 


E 




fO 


o . 


CO 


s: 


•i- DC 




+-> CO 


C\J 




3 

-— E 
O CD 


CNJ 
1 




CO 4-> 

to 






of Linear Drag 
Solution. Sy 


CD 




en 

E fO 


LO 




O S- 
tO Q 


LO 




Z. s_ 


^i- 




fO fO 


• 


Q. CD 




o 


E E 


1 


z 


O "1- 

O r— 


oo 


to 
to 




oo 
1 




£1 


C\J 




• 

CO 


CVJ 

1 




en 



o 

CM 



O 
O 



O 
CT> 



O 
00 



(6eug je9UL[U0N) uol^jo^slq 6uj.uds 'xew 
(Bguq ugsul-i) uol^Jo^slq 6uuds 'xew 



208 





"I 

• 1 


♦ 








>> 

u 


— 




• 


4 








c 

CU 

or QJ 
QJ CD 








^ 








S- L- 






• 


♦ 








CD 

31 







• 


4 












— 




Lf) 


























o 


o 
















• 


• 
















o 


o 
















II 


II 
















«/) 


10 
















CQ 


CQ 
















• 


♦ 












. 




























>> 
















O 
















e 








•« 








QJ 

a- qj 

QJ CD 


— 






. # 








s- e 








• ▼ 








a: 
■a 








•♦ 








S 


— 






• ♦ 
















4 


» 

♦J 






>> 
O 

c 

QJ 

3 

cr qj 


- 








••1 






QJ (J> 
S- e 
Li- ro 

a: 










| 






2 
O 
_l 


— 








| 








- 



o 






LO 




4-> 


LO 




1 E 
E QJ 


«^- 


• 


o e 




o 


z o 




z 


a. 


«*• 




-a E 


1 


to 


e o 


co 


to 

ro 


(0 o 


CO 


s: 


*-^oo 
>> i 


CM 




o « 


CM 




o o 






d by Ground Ve 
Earthquake, 19 


CD 

1 




QJ 
N O 


LO 




•i- S- 


LO 




rO E 
QJ QJ 


«3" 


o 


E O 




■21 


_J r— 


<n|- 
1 


to 


LU 


co 


to 


E 




rC 


O • 


ro 


s 


i- s: 




4-> 1^. 


CM 




3 

>— E 
O 0J 


CM 




oo +-> 
to 






of Linear Drag 
Solution. Sy 


CJ3 

1 




CD 
E ro 


LO 




O S- 
tO Q 


LO 






«=d- 


• 


fO n3 


o 


Q. QJ 




-zi 


E E 


«3- 




O f- 


i 


to 


O i— 


CO 


to 

n3 




CO 


s: 


CM 


CM 




CO 


CM 










CD 



o 

CM 



o 
o 



o 

CD 



O 
00 






(6ejQ jb9ul[uon) uol^jo^slq 6ut.jds 'xe^j 

(6BUQ JG9UL1) UOL^JO^SLQ 6UUd$ 'XPW 



209 



• 


j ♦ 
i ♦ 




'requency 
inge 

1 1 


• 


• ♦ 
• ♦ 








High F 
Re 

1 1 1 




i— LO 
O O 

O O 

II II 

to t/) 

OQ. 00. 

• ♦ 






i 










i 
i 

i 

i . # 






>> 
o 

c — 

O) 
O" cu 










1 • * 

• ♦ 




Mid Fn 
Ranc 

i i l 












« 


i 

♦ • 

i • * 


jency 






i 

i ♦• 

i •♦ 


Low Freqt 
Range 

i I 1 



CD 

I 







c cu 


*3- 


• 


o c 


o 


^ o 




z 


a. 


«tf- 




T3 E 


1 


to 


C O 


CO 


to 

03 


fO o 


co 


SL 


^- soo 

>> 1 


C\J 




•1 — 


C\J 

i 




o o 

I— *3- 






d by Ground Ve 
Earthquake, 19 


CD 




cu 

N O 


Lf) 




•r- S- 
S~ +■> 


lo 




03 C 
CU CU 


^t- 


• 


£Z CJ 




o 


•r™ 




z 


_J r— 


«3- 


to 


LU 


ro 


V) 


C 




03 


o • 


CO 


s 


•i- :n 




+-> r>. 


CsJ 




3 
r- E 

o cu 


C\J 
1 




CO +-> 
to 






of Linear Drag 
Solution. Sy 


CD 
1 




en 


IT) 




O S- 
to Q 


un 




•p— 


^~ 


d 


03 03 

Q. CU 




z 


E c 


^i- 




O T- 


i 


to 


O i— 


CO 


to 

03 




CO 
1 


s: 


co 


CsJ 




CO 


C\J 










en 



o 

CsJ 



o 
o 



o 

CM 



o 

CO 



(6eag jb9ul[uon) uol^jo^slq 6uuds *xew 
(6buq ueaun) uol^uo^slq buuds *xew 



210 



<L> 4- 

E 

Q) * 
(J "O 

fl3 E 
i — 3 
Q. O 
to S- 
•i- CD 
Q 

a> 
^ -C 
O -M 
<V 
O O 

Q. 

O QJ 
I— > 

E £ 

=5 rC 

E i— 

•i- a> 
x a: 

rO 





c 
< 


) a 


"Hpprt - Tnton 


^n+irt« M^ 










l/iiccl iMicyrauiuii - nu ur ay 

Direct Integration - Actual Drag 
^lodal Superposition - True Spectra 


4.0 


1 »l 


- Z.HD3 






♦ -♦Modal Superposition - True Spectra 

- SRSS 




3.5 

3.0 

2.5 

2.0 
1.5 








J 


1 










/ 
1 

1 
1 
1 












t 

1 
1 / 
1 / 
1 / 








/ 
/ 
/ 
/ 




> / ' 
' / < 

/ 


> 




4 


/ 
/ 

/ 

i ( 


"""V 


s 1 

* / 

/ 
{ 








i 


<x"*" 










1.0 




I 


1 1 


A 







400 



600 800 
Water Depth, ft 



1000 



Fig. 4.1 Response of Towers A, B, C, and D to El Centro 
Earthquake, 1940, N-S Component. B s = 0.01 



211 



Maximum Overturning Moment 
x 10 6 ft-kips 

ro co -P» en 

• • • • 

o o o o 








// 
// 






> 


k 


// 
// 

r 

' ■' 




i 


y 
s 

s 
< 

_ £^- — 




/ / 

' / ' 
'/' / 

It/ 

It/ 

/ / 










— o Direct I 

^ ni rort T 


/ / 
1/ 


m« n^^« 








riLcyraLIUil - nu ui a<-) 

ntegration - Actual Drag 

perposition - True Spectra 
S 

perposition - True Spectra 






Maximum Base Shear 
As % of Tower Weight 

ro en 
o en o 


♦- • 


- ZAB 
- -♦ Modal Su 


< 




- SRS 


S 








i 


i .. i 


1 A 


> 





400 



600 800 
Water Depth, ft 



1000 



Fig. 4.1 (Continued) 



212 



o 

o 







CD 

> 



V) 



.c 

4-> 

s_ 
o 

M- 

fO 

S- 

+J 
o 

o» 

Q. • 
OO <D 

<L) O 

c 

O -C 
Q. U 
</) rO 

<U LU 



4J O 

£ 
S- II 

o 

M— (/) 

<U CO. 
Q 

O • 
•r- <_> 
4-> 

to S_ 
A3 <D 
r- S 
UJ O 
I— 
T3 

N O 

i — t/1 
n3 CD 
<D "O 

-a O 



CVJ 



03S/NI 'UI3CTI3A 



213 



4.0 



3.5 



<U 

E +-> 

0; q_ 

O 

to " 

r- -O 

Q. C 

</> 3 

•r- O 

Q S- 

O (U 

CD -C 

Q. O 

O -t-> 

ai 

E > 

3 1- 

E +■> 

•f- (O 

X i— 

fO CD 



3.0 - 



2.5 - 



2.0 - 



1.5 



1.0 









/ 












/ 

/ 

/ 
/ 

/ 

/ 








/ 
/ 




/ 








/ 

/ 

/ 
/ 

/ 












/ 
/ 
/ / 


sgg^^ 






















■ 


1 


1 —J 


1 1 





400 



600 800 1000 
Water Depth, ft 



Fig. 4.3 Response of Towers A, B, C, and D 
Using Idealized Spectra 



214 



4-> 

C 
d) 



•i- -iii 

C I 

s- +-> 

=3 4- 

<U O 

> r— 
O 

X 



X 

<T3 



CD 



s- 


(D 


ia 


3 


0) 




SZ 


S_ 


oo 


O) 




2 


CD 


o 


00 I— 


(O 




CO 


4- 




o 


E 




Z5 


+J 


E 


c 


•r— 


O) 


X 


u 


03 


s- 


s: 


oj 




a. 




00 




n3 



6.0 



a) q. 5 n 



4.0 



3.0 - 



50 



25 



















IABS___ 


^ 
y 
^ 
s* 

^ 








/ 












/ 












/ 












/ 

/ 


SRSS 










/ / 














J%$ 










1 ' 


L .... _._. 1 




i 





400 



600 800 
Water Depth, ft 



Tooo" 



Fig. 4.3 (Continued) 



215 



VITA 

Owen Major Kirkley was born on 30 March 1936 in Washington, D. C. 
He attended schools in Texarkana, Arkansas and graduated from Arkansas High 
School in 1953. After attending the Rice Institute for one year, he entered 
the United States Naval Academy. He graduated from the Naval Academy in 
1958 with a Bachelor of Science degree and was commissioned an Ensign, Civil 
Engineer Corps, United States Navy. 

Following a short tour of duty at the U.S. Naval Air Station, 
Quonset Point, Rhode Island, he entered Rensselaer Polytechnic Institute and 
graduated with a Bachelor of Civil Engineering degree in 1960. After serving 
tours of duty with the U.S. Naval Administrative Unit Annex, Thurmont, Maryland, 
U.S. Naval Mobile Construction Battalion ONE, and the U.S. Navy Public Works 
Center, San Diego, California, he entered the University of Illinois in 1967. 
He received a Master of Science degree in civil engineering from the University 
of Illinois in 1968, and then served tours of duty with the Officer in Charge 
of Construction, Republic of Vietnam, Saigon, Vietnam and at the Headquarters, 
Naval Facilities Engineering Command, Washington, D. C. 

He is a registered Professional Engineer in the state of New York, 
is a member of the American Society of Civil Engineers, Tau Beta Pi, Chi 
Epsilon, Phi Kappa Phi, and Sigma Xi , and holds the rank of Commander, United 
States Navy. 



7 AUG 7.7 



S 1 n a 9 



Thesi s 
K516 



1^2037 



Kirkley 

Earthquake response 
of fixed offshore struc- 
tures. 
i IHM7'' DISPLAY- 

7AUG73 S10U97 









Thesis 1^2037 

K516 Kirkley 

Earthquake response 
of fixed offshore struc- 
tures. 



thesK516 

E MM«,?. Uake response of fixed offshore .• 




3 2768 002 10912 6 

DUDLEY KNOX LIBRARY